Journal articles: 'Pumping lemma'

1

Lu, Ruqian, and Hong Zheng. "Pumping Lemma for Quantum Automata." International Journal of Theoretical Physics 43, no. 5 (May 2004): 1191–217. http://dx.doi.org/10.1023/b:ijtp.0000048609.66662.87.

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Kászonyi, L. "A pumping lemma for DLI-languages." Discrete Mathematics 258, no. 1-3 (December 2002): 105–22. http://dx.doi.org/10.1016/s0012-365x(02)00265-0.

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3

Kostolányi, Peter. "A pumping lemma for flip-pushdown languages." RAIRO - Theoretical Informatics and Applications 50, no. 4 (June 2, 2016): 295–311. http://dx.doi.org/10.1051/ita/2016003.

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4

Colton, Don. "A restated pumping lemma for context-free languages." ACM SIGACT News 24, no. 2 (April 1993): 87. http://dx.doi.org/10.1145/156063.156066.

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Ewert, Sigrid, and Andries van der Walt. "A pumping lemma for random permitting context languages." Theoretical Computer Science 270, no. 1-2 (January 2002): 959–67. http://dx.doi.org/10.1016/s0304-3975(01)00171-2.

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6

Yu, Sheng. "A pumping lemma for deterministic context-free languages." Information Processing Letters 31, no. 1 (April 1989): 47–51. http://dx.doi.org/10.1016/0020-0190(89)90108-7.

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Gazdag, Zsolt, Krisztián Tichler, and Erzsébet Csuhaj-Varjú. "A Pumping Lemma for Permitting Semi-Conditional Languages." International Journal of Foundations of Computer Science 30, no. 01 (January 2019): 73–92. http://dx.doi.org/10.1142/s0129054119400045.

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Permitting semi-conditional grammars (pSCGs) are extensions of context-free grammars where each rule is associated with a word [Formula: see text] and such a rule can be applied to a sentential form [Formula: see text] only if [Formula: see text] is a subword of [Formula: see text]. We consider permitting generalized SCGs (pgSCGs) where each rule [Formula: see text] is associated with a set of words [Formula: see text] and [Formula: see text] is applicable only if every word in [Formula: see text] occurs in [Formula: see text]. We investigate the generative power of pgSCGs with no erasing rules and prove a pumping lemma for their languages. Using this lemma we show that pgSCGs are strictly weaker than context-sensitive grammars. This solves a long-lasting open problem concerning the generative power of pSCGs. Moreover, we give a comparison of the generating power of pgSCGs and that of forbidding random context grammars with no erasing rules.

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Fried, Michael N., and Mayer Goldberg. "A Pumping Lemma for Invalid Reductions of Fractions." College Mathematics Journal 41, no. 5 (November 2010): 357–64. http://dx.doi.org/10.4169/074683410x521955.

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MALETTI, ANDREAS. "RELATING TREE SERIES TRANSDUCERS AND WEIGHTED TREE AUTOMATA." International Journal of Foundations of Computer Science 16, no. 04 (August 2005): 723–41. http://dx.doi.org/10.1142/s012905410500325x.

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Bottom-up tree series transducers (tst) over the semiring [Formula: see text] are implemented with the help of bottom-up weighted tree automata (wta) over an extension of [Formula: see text]. Therefore bottom-up [Formula: see text]-weighted tree automata ([Formula: see text]-wta) with [Formula: see text] a distributive Ω-algebra are introduced. A [Formula: see text]-wta is essentially a wta but uses as transition weight an operation symbol of the Ω-algebra [Formula: see text] instead of a semiring element. The given tst is implemented with the help of a [Formula: see text]-wta, essentially showing that [Formula: see text]-wta are a joint generalization of tst (using IO-substitution) and wta. Then a semiring and a wta are constructed such that the wta computes a formal representation of the semantics of the [Formula: see text]-wta. The applicability of the obtained presentation result is demonstrated by deriving a pumping lemma for deterministic finite [Formula: see text]-wta from a known pumping lemma for deterministic finite wta. Finally, it is observed that the known decidability results for emptiness cannot be applied to obtain decidability of emptiness for finite [Formula: see text]-wta. Thus with help of a weaker version of the derived pumping lemma, decidability of the emptiness problem for finite [Formula: see text]-wta is shown under mild conditions on [Formula: see text].

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Ghorani, Maryam, Sunita Garhwal, and Somaye Moghari. "Lattice-valued tree pushdown automata: Pumping lemma and closure properties." International Journal of Approximate Reasoning 142 (March 2022): 301–23. http://dx.doi.org/10.1016/j.ijar.2021.12.002.

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Gal-Ezer, Judith, and Mark Trakhtenbrot. "Challenges in teaching the pumping lemma in automata theory course." ACM SIGCSE Bulletin 37, no. 3 (September 2005): 369. http://dx.doi.org/10.1145/1151954.1067569.

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12

Igarashi, Yoshihide. "A pumping lemma for real-time deterministic context-free languages." Theoretical Computer Science 36 (1985): 89–97. http://dx.doi.org/10.1016/0304-3975(85)90032-5.

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13

Balanescu, Tudor, and Marian Gheorghe. "A Note on Pf(k) – Parsable Languages." Fundamenta Informaticae 14, no. 3 (March 1, 1991): 283–86. http://dx.doi.org/10.3233/fi-1991-14302.

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This paper investigates the class of regular languages which are pf(k) – parsable. It is shown that k induces an infinite hierarchy in the family of regular languages and that every regular language is a homomorphic image of a pf(O) -parsable language. A pumping lemma for pf – parsable languages is also provided.

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14

Kanazawa, Makoto, Gregory M. Kobele, Jens Michaelis, Sylvain Salvati, and Ryo Yoshinaka. "The Failure of the Strong Pumping Lemma for Multiple Context-Free Languages." Theory of Computing Systems 55, no. 1 (January 30, 2014): 250–78. http://dx.doi.org/10.1007/s00224-014-9534-z.

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15

BalaPrakasaRao, K., B. Venu Gopal, and R. Kanaka Raju. "On Pumping lemma for Regular and Context free Lan-guages and Ogden's Lemma for Context free Lan-guages." International Journal of Computer Applications 39, no. 10 (February 29, 2012): 53–59. http://dx.doi.org/10.5120/4860-7137.

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16

Singh, Anupam K., and S. P. Tiwari. "Fuzzy Regular Languages Based on Residuated Lattice." New Mathematics and Natural Computation 16, no. 02 (July 2020): 363–76. http://dx.doi.org/10.1142/s1793005720500222.

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The purpose of this work is to introduce the concept of fuzzy regular languages (FRL) accepted by fuzzy finite automata, and try to introduce the categorical look of fuzzy languages where the codomain of membership functions are taken as a complete residuated lattice, instead of [Formula: see text]. Also, we have introduced pumping lemma for FRL, which is used to establish a necessary and sufficient condition for a given fuzzy languages to be non-constant.

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SAOUDI, A., K. RANGARAJAN, and V. R. DARE. "FINITE IMAGES GENERATED BY GL-SYSTEMS." International Journal of Pattern Recognition and Artificial Intelligence 03, no. 03n04 (December 1989): 459–67. http://dx.doi.org/10.1142/s0218001489000346.

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In this paper, we introduce a new device called GL-systems (i.e. Grammar-Lindenmayer systems) for generating finite images. GL-systems are sequential/parallel systems in which the horizontal rules form a Chomskian grammar and the vertical rules form a DTOL system. We obtain hierarchical results of various types of GL-systems. We study some properties like, closure properties, combinatorial results, pumping lemma and decidability results. An algebraic characterization for GL-systems (with variation) is presented.

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Ramos, Marcus V. M., José Carlos Bacelar Almeida, Nelma Moreira, and Ruy J. G. B. de Queiroz. "Some Applications of the Formalization of the Pumping Lemma for Context-Free Languages." Electronic Notes in Theoretical Computer Science 344 (August 2019): 151–67. http://dx.doi.org/10.1016/j.entcs.2019.07.010.

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19

Smith, Tim. "A new pumping lemma for indexed languages, with an application to infinite words." Information and Computation 252 (February 2017): 176–86. http://dx.doi.org/10.1016/j.ic.2016.11.002.

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BREVEGLIERI, LUCA, ALESSANDRA CHERUBINI, CLAUDIO CITRINI, and STEFANO CRESPI REGHIZZI. "MULTI-PUSH-DOWN LANGUAGES AND GRAMMARS." International Journal of Foundations of Computer Science 07, no. 03 (September 1996): 253–91. http://dx.doi.org/10.1142/s0129054196000191.

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A new class of languages, called multi-push-down (mpd), that generalize the classical context-free (cf, or Chomsky type 2) ones is introduced. These languages preserve some important properties of cf languages: a generalization of the Chomsky-Schützenberger homomorphic characterization theorem, the Parikh theorem and a “pumping lemma” are proved. Multi-push-down languages are an AFL. Their recognizers are automata equipped with a multi-push-down tape. Multi-push-down languages form a hierarchy based on the number of push-down tapes.

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Qiu, Daowen. "Pumping lemma in automata theory based on complete residuated lattice-valued logic: A note." Fuzzy Sets and Systems 157, no. 15 (August 2006): 2128–38. http://dx.doi.org/10.1016/j.fss.2006.03.014.

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Xing, Hongyan, and Daowen Qiu. "Pumping lemma in context-free grammar theory based on complete residuated lattice-valued logic." Fuzzy Sets and Systems 160, no. 8 (April 2009): 1141–51. http://dx.doi.org/10.1016/j.fss.2008.06.016.

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Yamazaki, Koichi, and Takeo Yaku. "A Pumping lemma and the structure of derivations in the boundary NLC graph languages." Information Sciences 75, no. 1-2 (December 1993): 81–97. http://dx.doi.org/10.1016/0020-0255(93)90114-2.

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González de Mendívil, José R., and José R. Garitagoitia. "Fuzzy languages with infinite range accepted by fuzzy automata: Pumping Lemma and determinization procedure." Fuzzy Sets and Systems 249 (August 2014): 1–26. http://dx.doi.org/10.1016/j.fss.2014.02.006.

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25

Chytil, Michal P. "Almost Context-Free Languages." Fundamenta Informaticae 9, no. 3 (July 1, 1986): 283–321. http://dx.doi.org/10.3233/fi-1986-9303.

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We define a superclass of the class of context-free languages, denoted ACFL (almost context-free languages) and construct an infinite sequence of non-context-free languages of decreasing complexity, belonging to ACFL. The languages in ACFL share many important properties of context-free languages. For example, a slight generalization of pumping lemma for context-free languages holds also for languages in ACFL. Similarly, some of the questions decidable for context-free languages are decidable in ACFL and start to be undecidable immediately outside the class. ACFL is a full AFL and contains an infinite strictly decreasing chain of full AFLs.

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CÂMPEANU, CEZAR, KAI SALOMAA, and SHENG YU. "A FORMAL STUDY OF PRACTICAL REGULAR EXPRESSIONS." International Journal of Foundations of Computer Science 14, no. 06 (December 2003): 1007–18. http://dx.doi.org/10.1142/s012905410300214x.

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Regular expressions are used in many practical applications. Practical regular expressions are commonly called "regex". It is known that regex are different from regular expressions. In this paper, we give regex a formal treatment. We make a distinction between regex and extended regex; while regex represent regular languages, extended regex represent a family of languages larger than regular languages. We prove a pumping lemma for the languages expressed by extended regex. We show that the languages represented by extended regex are incomparable with context-free languages and a proper subset of context-sensitive languages. Other properties of the languages represented by extended regex are also studied.

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EWERT, SIGRID, and ANDRIES VAN DER WALT. "A HIERARCHY RESULT FOR RANDOM FORBIDDING CONTEXT PICTURE GRAMMARS." International Journal of Pattern Recognition and Artificial Intelligence 13, no. 07 (November 1999): 997–1007. http://dx.doi.org/10.1142/s0218001499000550.

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We use random context picture grammars to generate pictures through successive refinement. The productions of such a grammar are context-free, but their application is regulated — "permitted" or "forbidden" — by context randomly distributed in the developing picture. Grammars using this relatively weak context often succeed where context-free grammars fail, e.g. in generating the Sierpiński carpets. On the other hand it proved possible to develop iteration theorems for three subclasses of these grammars, namely a pumping–shrinking, a pumping and a shrinking lemma for context-free, random permitting and random forbidding context picture grammars, respectively. Finding necessary conditions is problematic in the case of most models of context-free grammars with context-sensing ability, since they consider a variable and its context as a finite connected array. We have already shown that context-free picture grammars are strictly weaker than both random permitting and random forbidding context picture grammars, also that random permitting context is strictly weaker than random context. We now show that grammars which use forbidding context only are strictly weaker than random context picture grammars.

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Chigahara, Hiroyuki, Szilárd Zsolt Fazekas, and Akihiro Yamamura. "One-Way Jumping Finite Automata." International Journal of Foundations of Computer Science 27, no. 03 (February 2016): 391–405. http://dx.doi.org/10.1142/s0129054116400165.

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We propose the one-way jumping finite automaton model, restricting the jumping relation of the recently introduced jumping finite automaton so that the machine can only jump over symbols it cannot process in its current state. The reading head of a one-way jumping finite automaton moves deterministically in one direction within the input word, whereas movement of the reading head of jumping finite automaton is non-deterministic. The class of languages accepted by one-way jumping finite automata is different from that of jumping finite automata, in particular, it includes all regular languages, as opposed to the latter. We study one-way jumping finite automata and obtain closure properties, a pumping lemma, and separation results with respect to the classical language classes of the Chomsky hierarchy.

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EWERT, SIGRID, and ANDRIES VAN DER WALT. "GENERATING PICTURES USING RANDOM PERMITTING CONTEXT." International Journal of Pattern Recognition and Artificial Intelligence 13, no. 03 (May 1999): 339–55. http://dx.doi.org/10.1142/s0218001499000197.

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We use random context picture grammars to generate pictures through successive refinement. At any stage a picture consists of a shape divided into smaller shapes, each containing a variable or terminal. A variable may be rewritten according to a production of the underlying grammar, which entails either dividing the shape containing it into smaller shapes, or substituting a variable or terminal for it. A production may depend on context randomly distributed in the intermediate picture. Context is classified as either permitting or forbidding, the former enabling the application of a production, the latter inhibiting it. For visualization purposes every terminal is associated with a color, and its shape filled with that color. We show examples of pictures generated with random context picture grammars. Then we concentrate on grammars which use permitting context only and present a pumping lemma for the corresponding picture sets.

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Jin, Jianhua, Qingguo Li, and Chunquan Li. "On Intuitionistic Fuzzy Context-Free Languages." Journal of Applied Mathematics 2013 (2013): 1–16. http://dx.doi.org/10.1155/2013/825249.

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Taking intuitionistic fuzzy sets as the structures of truth values, we propose the notions of intuitionistic fuzzy context-free grammars (IFCFGs, for short) and pushdown automata with final states (IFPDAs). Then we investigate algebraic characterization of intuitionistic fuzzy recognizable languages including decomposition form and representation theorem. By introducing the generalized subset construction method, we show that IFPDAs are equivalent to their simple form, called intuitionistic fuzzy simple pushdown automata (IF-SPDAs), and then prove that intuitionistic fuzzy recognizable step functions are the same as those accepted by IFPDAs. It follows that intuitionistic fuzzy pushdown automata with empty stack and IFPDAs are equivalent by classical automata theory. Additionally, we introduce the concepts of Chomsky normal form grammar (IFCNF) and Greibach normal form grammar (IFGNF) based on intuitionistic fuzzy sets. The results of our study indicate that intuitionistic fuzzy context-free languages generated by IFCFGs are equivalent to those generated by IFGNFs and IFCNFs, respectively, and they are also equivalent to intuitionistic fuzzy recognizable step functions. Then some operations on the family of intuitionistic fuzzy context-free languages are discussed. Finally, pumping lemma for intuitionistic fuzzy context-free languages is investigated.

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RAVIKUMAR, BALA. "THE BENFORD-NEWCOMB DISTRIBUTION AND UNAMBIGUOUS CONTEXT-FREE LANGUAGES." International Journal of Foundations of Computer Science 19, no. 03 (June 2008): 717–27. http://dx.doi.org/10.1142/s0129054108005905.

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For a string w ∈ {0,1, 2,…, d-1}*, let vald(w) denote the integer whose base d representation is the string w and let MSDd(x) denote the most significant or the leading digit of a positive integer x when x is written as a base d integer. Hirvensalo and Karhumäki [9] studied the problem of computing the leading digit in the ternary representation of 2x ans showed that this problem has a polynomial time algorithm. In [16], some applications are presented for the problem of computing the leading digit of AB for given inputs A and B. In this paper, we study this problem from a formal language point of view. Formally, we consider the language Lb,d,j = {w|w ∈ {0,1, 2,…, d-1}*, 1 ≤ j ≤ 9, MSDb(dvalb(w))) = j} (and some related classes of languages) and address the question of whether this and some related languages are context-free. Standard pumping lemma proofs seem to be very difficult for these languages. We present a unified and simple combinatorial technique that shows that these languages are not unambiguous context-free languages. The Benford-Newcomb distribution plays a central role in our proofs.

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Johnsonbaugh, Richard, and David P. Miller. "Converses of pumping lemmas." ACM SIGCSE Bulletin 22, no. 1 (February 1990): 27–30. http://dx.doi.org/10.1145/319059.319073.

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Palis, M. A., and S. M. Shende. "Pumping lemmas for the control language hierarchy." Mathematical Systems Theory 28, no. 3 (May 1995): 199–213. http://dx.doi.org/10.1007/bf01303055.

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Ressayre, J. P. "Formal languages defined by the underlying structure of their words." Journal of Symbolic Logic 53, no. 4 (December 1988): 1009–26. http://dx.doi.org/10.1017/s0022481200027894.

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Abstracti) We show for each context-free language L that by considering each word of L as a structure in a natural way, one turns L into a finite union of classes which satisfy a finitary analog of the characteristic properties of complete universal first order classes of structures equipped with elementary embeddings. We show this to hold for a much larger class of languages which we call free local languages, ii) We define local languages, a class of languages between free local and context-sensitive languages. Each local language L has a natural extension L∞ to infinite words, and we prove a series of “pumping lemmas”, analogs for each local language L of the “uvxyz theorem” of context free languages: they relate the existence of large words in L or L∞ to the existence of infinite “progressions” of words included in L, and they imply the decidability of various questions about L or L∞. iii) We show that the pumping lemmas of ii) are independent from strong axioms, ranging from Peano arithmetic to ZF + Mahlo cardinals.We hope that these results are useful for a model-theoretic approach to the theory of formal languages.

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NIVAT, M., A. SAOUDI, and V. R. DARE. "PARALLEL GENERATION OF FINITE IMAGES." International Journal of Pattern Recognition and Artificial Intelligence 03, no. 03n04 (December 1989): 279–94. http://dx.doi.org/10.1142/s0218001489000243.

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We define a syntactic model for generating sets of images, where an image can be viewed as an array over finite alphabet. This model is called image grammar. Image grammar can be considered as a generalization of classical Chomsky grammar. Then we study some combinatorial and language theoretical properties such as reduction, pumping lemmas, complexity measure, we give a strict infinite hierarchy. We also characterize these families in terms of deterministic substitutions and Chomsky languages.

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Verma, Payal, Nilesh Thaokar, and Raymond Andrew. "Hatching in Coromandel Marsh Dart Damselfly Ceriagrion coromandelianum (Fabricius) (Zygoptera: Coenagrionidae): process and influence of the oviposition substrate." Journal of Threatened Taxa 14, no. 4 (April 26, 2022): 20840–47. http://dx.doi.org/10.11609/jott.6455.14.4.20840-20847.

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Coromandel Marsh Dart Damselfly Ceriagrion coromandelianum (Fabricius) breeds in stagnant pools, small garden tanks and ornamental cement ponds containing submerged and/or floating vegetation. Eggs were collected to observe two aspects of larval development: (1) The hatching rate of eggs deposited in different vegetation (Nymphaea nouchali, Lemna paucicostata, Hydrilla verticillata). Although C. coromandelianum prefers to oviposit in the broad leaves of N. nouchali, the highest rate of hatching was found in H. verticillata (95.8%) followed by N. nouchali (87.6%) and L. paucicostata (81.3%). Hatching commenced on Day 5 and was completed by Day 9. Maximum hatching (56%) was recorded on the sixth day of oviposition followed by the seventh day (20%) in all three substrates. (2) To document the process of hatching as follows: Around three minutes prior to hatching, the embryo exhibits cyclic pumping and pushing movements of the head (caused by the peristaltic movement of the mid- and hind- gut) of low intensity followed by high intensity and long pumping movements interspaced with smaller pulsating movements. Swelling of the head forces the apical chorion to split along the micropylar chute and like a lid, the apical tip topples over as a conical cap. This allows the prolarva to exit the egg. As it does so, it twists and the thorax swells breaking the prolarval sheath and releasing the first instar larva.

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Verma, Payal, Nilesh Thaokar, and Raymond Andrew. "Hatching in Coromandel Marsh Dart Damselfly Ceriagrion coromandelianum (Fabricius) (Zygoptera: Coenagrionidae): process and influence of the oviposition substrate." Journal of Threatened Taxa 14, no. 4 (April 26, 2022): 20840–47. http://dx.doi.org/10.11609/jott.6455.14.4.20840-20847.

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Coromandel Marsh Dart Damselfly Ceriagrion coromandelianum (Fabricius) breeds in stagnant pools, small garden tanks and ornamental cement ponds containing submerged and/or floating vegetation. Eggs were collected to observe two aspects of larval development: (1) The hatching rate of eggs deposited in different vegetation (Nymphaea nouchali, Lemna paucicostata, Hydrilla verticillata). Although C. coromandelianum prefers to oviposit in the broad leaves of N. nouchali, the highest rate of hatching was found in H. verticillata (95.8%) followed by N. nouchali (87.6%) and L. paucicostata (81.3%). Hatching commenced on Day 5 and was completed by Day 9. Maximum hatching (56%) was recorded on the sixth day of oviposition followed by the seventh day (20%) in all three substrates. (2) To document the process of hatching as follows: Around three minutes prior to hatching, the embryo exhibits cyclic pumping and pushing movements of the head (caused by the peristaltic movement of the mid- and hind- gut) of low intensity followed by high intensity and long pumping movements interspaced with smaller pulsating movements. Swelling of the head forces the apical chorion to split along the micropylar chute and like a lid, the apical tip topples over as a conical cap. This allows the prolarva to exit the egg. As it does so, it twists and the thorax swells breaking the prolarval sheath and releasing the first instar larva.

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Steiner, Jean L., Daniel L. Devlin, Sam Perkins, Jonathan P. Aguilar, Bill Golden, Eduardo A. Santos, and Matt Unruh. "Policy, Technology, and Management Options for Water Conservation in the Ogallala Aquifer in Kansas, USA." Water 13, no. 23 (December 2, 2021): 3406. http://dx.doi.org/10.3390/w13233406.

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The Ogallala Aquifer underlies 45 million ha, providing water for approximately 1.9 million people and supporting the robust agriculture economy of the US Great Plains region. The Ogallala Aquifer has experienced severe depletion, particularly in the Southern Plains states. This paper presents policy innovations that promote adoption of irrigation technology, and management innovations. Innovation in Kansas water policy has had the dual effects of increasing the authority of the state to regulate water while also providing more flexibility and increasing local input to water management and regulation. Technology innovations have focused on improved timing and placement of water. Management innovations include soil water monitoring, irrigation scheduling, soil health management and drought-tolerant varieties, crops, and cropping systems. The most noted success has been in the collective action which implemented a Local Enhanced Management Area (LEMA), which demonstrated that reduced water pumping resulted in low to no groundwater depletion while maintaining net income. Even more encouraging is the fact that irrigators who have participated in the LEMA or other conservation programs have conserved even more water than their goals. Innovative policy along with creative local–state–federal and private–public partnerships are advancing irrigation technology and management. Flexibility through multi-year allocations, banking of water not used in a given year, and shifting water across multiple water rights or uses on a farm are promising avenues to engage irrigators toward more sustainable irrigation in the Ogallala region.

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Das, S., A. Koner, and A. Barik. "Biology and life history of Lema praeusta (Fab.) (Coleoptera: Chrysomelidae), a biocontrol agent of two Commelinaceae weeds, Commelina benghalensis and Murdannia nudiflora." Bulletin of Entomological Research 109, no. 4 (October 4, 2018): 463–71. http://dx.doi.org/10.1017/s0007485318000731.

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AbstractWe examined previous reports of Lema praeusta (Fab.) (Coleoptera: Chrysomelidae) as a minor pest of turmeric, eggplant, bottle gourd and pumpkin leaves, but no feeding damage by larvae and adults of L. praeusta were recorded by us on these leaves. We observed feeding by the larvae and adults of L. praeusta on ten species of Commelinaceae plants in no-choice tests. The biology, fecundity and life table parameters of L. praeusta on two Commelinaceae weeds, Commelina benghalensis L. and Murdannia nudiflora (L.) Brenan were determined under laboratory conditions (27 ± 1°C, 65 ± 5% RH and 12L:12D). Total larval development times of L. praeusta were 6.36 ± 0.07 and 7.28 ± 0.11 days (mean ± SE) on C. benghalensis and M. nudiflora, respectively. Adult females lived 106.25 ± 1.17 and 77.65 ± 0.91 days (mean ± SE) on C. benghalensis and M. nudiflora, respectively. Each female laid 272.95 ± 2.39 and 224 ± 1.74 eggs (mean ± SE) during a lifetime on C. benghalensis and M. nudiflora, respectively. The net reproductive rate (Ro), intrinsic rate of increase (rm), generation time (Tc), doubling time (DT) and finite rate of increase (λ) were 136.48, 0.14, 36.17, 5.10 and 1.41 on C. benghalensis, respectively, whereas Ro, rm, Tc, DT and λ were 112, 0.20, 23.64, 3.47 and 1.51 on M. nudiflora, respectively, suggesting that L. praeusta could be a potential biocontrol agent against C. benghalensis and M. nudiflora in the fields of rice, maize, sorghum, soybean, mung bean, peanut and cotton.

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"A pumping lemma for monotonous super-nets languages." Decision Support Systems 2, no. 3 (September 1986): 276. http://dx.doi.org/10.1016/0167-9236(86)90069-2.

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41

Dassow, Jürgen, and Ismaël Jecker. "Operational complexity and pumping lemmas." Acta Informatica, July 20, 2022. http://dx.doi.org/10.1007/s00236-022-00431-3.

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AbstractThe well-known pumping lemma for regular languages states that, for any regular language L, there is a constant p (depending on L) such that the following holds: If $$w\in L$$ w ∈ L and $$\vert w\vert \ge p$$ | w | ≥ p , then there are words $$x\in V^{*}$$ x ∈ V ∗ , $$y\in V^+$$ y ∈ V + , and $$z\in V^{*}$$ z ∈ V ∗ such that $$w=xyz$$ w = x y z and $$xy^tz\in L$$ x y t z ∈ L for $$t\ge 0$$ t ≥ 0 . The minimal pumping constant $${{{\,\mathrm{mpc}\,}}(L)}$$ mpc ( L ) of L is the minimal number p for which the conditions of the pumping lemma are satisfied. We investigate the behaviour of $${{{\,\mathrm{mpc}\,}}}$$ mpc with respect to operations, i. e., for an n-ary regularity preserving operation $$\circ $$ ∘ , we study the set $${g_{\circ }^{{{\,\mathrm{mpc}\,}}}(k_1,k_2,\ldots ,k_n)}$$ g ∘ mpc ( k 1 , k 2 , … , k n ) of all numbers k such that there are regular languages $$L_1,L_2,\ldots ,L_n$$ L 1 , L 2 , … , L n with $${{{\,\mathrm{mpc}\,}}(L_i)=k_i}$$ mpc ( L i ) = k i for $$1\le i\le n$$ 1 ≤ i ≤ n and $${{{\,\mathrm{mpc}\,}}(\circ (L_1,L_2,\ldots ,L_n)=~k}$$ mpc ( ∘ ( L 1 , L 2 , … , L n ) = k . With respect to Kleene closure, complement, reversal, prefix and suffix-closure, circular shift, union, intersection, set-subtraction, symmetric difference,and concatenation, we determine $${g_{\circ }^{{{\,\mathrm{mpc}\,}}}(k_1,k_2,\ldots ,k_n)}$$ g ∘ mpc ( k 1 , k 2 , … , k n ) completely. Furthermore, we give some results with respect to the minimal pumping length where, in addition, $$\vert xy\vert \le p$$ | x y | ≤ p has to hold.

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42

Koga, Toshihiro. "A Pumping Lemma for Regular Closure of Prefix-free Languages." Information and Computation, October 2022, 104976. http://dx.doi.org/10.1016/j.ic.2022.104976.

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43

Gautam, Vinay. "l-Valued multiset automata and l-valued multiset languages." New Mathematics and Natural Computation, December 19, 2020, 1–15. http://dx.doi.org/10.1142/s1793005721500095.

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The reason for this work is to present and study deterministic multiset automata, multiset automata and their languages with membership values in complete residuated lattice without zero divisors. We build up the comparability of deterministic [Formula: see text]-valued multiset finite automaton and [Formula: see text]-valued multiset finite automaton in sense of recognizability of a [Formula: see text]-valued multiset language. Then, we relate multiset regular languages to a given [Formula: see text]-valued multiset regular languages and vice versa. At last, we present the concept of pumping lemma for [Formula: see text]-valued multiset automata theory, which we utilize to give a necessary and sufficient condition for a [Formula: see text]-valued multiset language to be non-constant.

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44

Kitaev, Sergey, Jeffrey Liese, Jeffrey Remmel, and Bruce E. Sagan. "Rationality, Irrationality, and Wilf Equivalence in Generalized Factor Order." Electronic Journal of Combinatorics 16, no. 2 (December 2, 2009). http://dx.doi.org/10.37236/88.

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Let $P$ be a partially ordered set and consider the free monoid $P^*$ of all words over $P$. If $w,w'\in P^*$ then $w'$ is a factor of $w$ if there are words $u,v$ with $w=uw'v$. Define generalized factor order on $P^*$ by letting $u\le w$ if there is a factor $w'$ of $w$ having the same length as $u$ such that $u\le w'$, where the comparison of $u$ and $w'$ is done componentwise using the partial order in $P$. One obtains ordinary factor order by insisting that $u=w'$ or, equivalently, by taking $P$ to be an antichain. Given $u\in P^*$, we prove that the language ${\cal F}(u)=\{w\ :\ w\ge u\}$ is accepted by a finite state automaton. If $P$ is finite then it follows that the generating function $F(u)=\sum_{w\ge u} w$ is rational. This is an analogue of a theorem of Björner and Sagan for generalized subword order. We also consider $P={\Bbb P}$, the positive integers with the usual total order, so that $P^*$ is the set of compositions. In this case one obtains a weight generating function $F(u;t,x)$ by substituting $tx^n$ each time $n\in{\Bbb P}$ appears in $F(u)$. We show that this generating function is also rational by using the transfer-matrix method. Words $u,v$ are said to be Wilf equivalent if $F(u;t,x)=F(v;t,x)$ and we prove various Wilf equivalences combinatorially. Björner found a recursive formula for the Möbius function of ordinary factor order on $P^*$. It follows that one always has $\mu(u,w)=0,\pm1$. Using the Pumping Lemma we show that the generating function $M(u)=\sum_{w\ge u} |\mu(u,w)| w$ can be irrational.

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45

Chattopadhyay, Agnishom, Filip Mazowiecki, Anca Muscholl, and Cristian Riveros. "Pumping lemmas for weighted automata." Logical Methods in Computer Science Volume 17, Issue 3 (July 21, 2021). http://dx.doi.org/10.46298/lmcs-17(3:7)2021.

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We present pumping lemmas for five classes of functions definable by fragments of weighted automata over the min-plus semiring, the max-plus semiring and the semiring of natural numbers. As a corollary we show that the hierarchy of functions definable by unambiguous, finitely-ambiguous, polynomially-ambiguous weighted automata, and the full class of weighted automata is strict for the min-plus and max-plus semirings.

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46

Lucero, Jorge C. "Pumping lemmas for classes of languages generated by folding systems." Natural Computing, October 26, 2019. http://dx.doi.org/10.1007/s11047-019-09771-5.

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47

Kitaev, Sergey, Jeffrey Liese, Jeffrey Remmel, and Bruce Sagan. "Rationality, irrationality, and Wilf equivalence in generalized factor order." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings vol. AK,..., Proceedings (January 1, 2009). http://dx.doi.org/10.46298/dmtcs.2688.

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International audience Let $P$ be a partially ordered set and consider the free monoid $P^{\ast}$ of all words over $P$. If $w,w' \in P^{\ast}$ then $w'$ is a factor of $w$ if there are words $u,v$ with $w=uw'v$. Define generalized factor order on $P^{\ast}$ by letting $u \leq w$ if there is a factor $w'$ of $w$ having the same length as $u$ such that $u \leq w'$, where the comparison of $u$ and $w'$ is done componentwise using the partial order in $P$. One obtains ordinary factor order by insisting that $u=w'$ or, equivalently, by taking $P$ to be an antichain. Given $u \in P^{\ast}$, we prove that the language $\mathcal{F}(u)=\{w : w \geq u\}$ is accepted by a finite state automaton. If $P$ is finite then it follows that the generating function $F(u)=\sum_{w \geq u} w$ is rational. This is an analogue of a theorem of Björner and Sagan for generalized subword order. We also consider $P=\mathbb{P}$, the positive integers with the usual total order, so that $\mathbb{P}^{\ast}$ is the set of compositions. In this case one obtains a weight generating function $F(u;t,x)$ by substituting $tx^n$ each time $n \in \mathbb{P}$ appears in $F(u)$. We show that this generating function is also rational by using the transfer-matrix method. Words $u,v$ are said to be Wilf equivalent if $F(u;t,x)=F(v;t,x)$ and we can prove various Wilf equivalences combinatorially. Björner found a recursive formula for the Möbius function of ordinary factor order on $P^{\ast}$. It follows that one always has $\mu (u,w)=0, \pm 1$. Using the Pumping Lemma we show that the generating function $M(u)= \sum_{w \geq u} | \mu (u,w) | w$ can be irrational. Soit $P$ un ensemble partiellement ordonné. Nous considérons le monoïde libre $P^{\ast}$ de tous les mots utilisant $P$ comme alphabet. Si $w,w' \in P^{\ast}$, on dit que $w'$ est un facteur de $w$ s'il y a des mots $u,v$ avec $w=uw'v$. Nous définissons l'ordre facteur généralisé sur $P^{\ast}$ par: $u \leq w$ s'il y a un facteur $w'$ de $w$ ayant la même longueur que $u$ tel que $u \leq w'$, où la comparaison de $u$ avec $w'$ est faite lettre par lettre utilisant l'ordre en $P$. On obtient l'ordre facteur usuel si on insiste que $u=w'$ ou, ce qui est la même chose, en prenant $P$ comme antichaîne. Pour n'importe quel $u \in P^{\ast}$, nous démontrons que le langage $\mathcal{F}(u)=\{w : w \geq u\}$ est accepté par un automaton avec un nombre fini d'états. Si $P$ est fini, ça implique que la fonction génératrice $F(u)=\sum_{w \geq u} w$ est rationnelle. Björner et Sagan ont démontré le théorème analogue pour l'ordre où, en la définition au-dessus, $w'$ est un sous-mot de $w$. Nous considérons aussi le cas $P=\mathbb{P}$, les entiers positifs avec l'ordre usuel, donc $P^{\ast}$ est l'ensemble des compositions. En ce cas on obtient une fonction génératrice pondéré $F(u;t,x)$ en remplaçant $tx^n$ chaque fois on trouve $n \in \mathbb{P}$ en $F(u)$. Nous démontrons que cette fonction génératrice est aussi rationnelle en utilisant la Méthode Matrice de Tranfert. On dit que let mots $u,v$ sont Wilf-équivalents si $F(u;t,x)=F(v;t,x)$. Nous pouvons démontré quelques équivalences dans une manière combinatoire. Björner a trouvé une formule récursive pour la fonction Möbius de l'ordre facteur usuel sur $P^{\ast}$. Cette formule implique qu'on a toujours $\mu (u,w)=0, \pm 1$. En utilisant le Lemme de Pompage, nous démontrons que la fonction génératrice $M(u)= \sum_{w \geq u} | \mu (u,w) | w$ peut être irrationnelle.

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