Academic literature on the topic 'CHC solver'

AbstractWe address the problem of verifying the satisfiability of Constrained Horn Clauses (CHCs) based on theories of inductively defined data structures, such as lists and trees. We propose a transformation technique whose objective is the removal of these data structures from CHCs, hence reducing their satisfiability to a satisfiability problem for CHCs on integers and booleans. We propose a transformation algorithm and identify a class of clauses where it always succeeds. We also consider an extension of that algorithm, which combines clause transformation with reasoning on integer constraints. Via an experimental evaluation we show that our technique greatly improves the effectiveness of applying the Z3 solver to CHCs. We also show that our verification technique based on CHC transformation followed by CHC solving, is competitive with respect to CHC solvers extended with induction.

Solving reachability games is a fundamental problem for the analysis, verification, and synthesis of reactive systems. We consider logical reachability games modulo theories (in short, GMTs), i.e., infinite-state games whose rules are defined by logical formulas over a multi-sorted first-order theory. Our games have an asymmetric constraint: the safety player has at most k possible moves from each game configuration, whereas the reachability player has no such limitation. Even though determining the winner of such a GMT is undecidable, it can be reduced to the well-studied problem of checking the satisfiability of a system of constrained Horn clauses (CHCs), for which many off-the-shelf solvers have been developed. Winning strategies for GMTs can also be computed by resorting to suitable CHC queries. We demonstrate that GMTs can model various relevant real-world games, and that our approach can effectively solve several problems from different domains, using Z3 as the backend CHC solver.

Property Directed Reachability (PDR) is an efficient and scalable approach to solving systems of symbolic constraints also known as Constrained Horn Clauses (CHC). In the case of non-linear CHCs, which may arise, e.g., from relational verification tasks, PDR aims to infer an inductive invariant for each uninterpreted predicate. However, in many practical cases this reasoning is not successful, as invariants should be derived for groups of predicates instead of individual predicates. The article describes a novel algorithm that identifies these groups automatically and complements the existing PDR technique. The key feature of the algorithm is that it does not require a possibly expensive synchronization transformation over the system of CHCs. We have implemented the algorithm on top of a up-to-date CHC solver Spacer. Our experimental evaluation shows that for some CHC systems, on which existing solvers diverge, our tool is able to discover relational invariants.

The Chebyshev collocation method implemented in Chebfun is used in order to solve a class of second order one-dimensional singular and genuinely nonlinear boundary value problems. Efforts to solve these problems with conventional ChC have generally failed, and the outcomes obtained by finite differences or finite elements are seldom satisfactory. We try to fix this situation using the new Chebfun programming environment. However, for tough problems, we have to loosen the default Chebfun tolerance in Newton’s solver as the ChC runs into trouble with ill-conditioning of the spectral differentiation matrices. Although in such cases the convergence is not quadratic, the Newton updates decrease monotonically. This fact, along with the decreasing behaviour of Chebyshev coefficients of solutions, suggests that the outcomes are trustworthy, i.e., the collocation method has exponential (geometric) rate of convergence or at least an algebraic rate. We consider first a set of problems that have exact solutions or prime integrals and then another set of benchmark problems that do not possess these properties. Actually, for each test problem carried out we have determined how the Chebfun solution converges, its length, the accuracy of the Newton method and especially how well the numerical results overlap with the analytical ones (existence and uniqueness).

AbstractIt is well-known that the verification of partial correctness properties of imperative programs can be reduced to the satisfiability problem for constrained Horn clauses (CHCs). However, state-of-the-art solvers for constrained Horn clauses (or CHC solvers) based onpredicate abstractionare sometimes unable to verify satisfiability because they look for models that are definable in a given class 𝓐 of constraints, called 𝓐-definable models. We introduce a transformation technique, calledPredicate Pairing, which is able, in many interesting cases, to transform a set of clauses into an equisatisfiable set whose satisfiability can be proved by finding an 𝓐-definable model, and hence can be effectively verified by a state-of-the-art CHC solver. In particular, we prove that, under very general conditions on 𝓐, the unfold/fold transformation rules preserve the existence of an 𝓐-definable model, that is, if the original clauses have an 𝓐-definable model, then the transformed clauses have an 𝓐-definable model. The converse does not hold in general, and we provide suitable conditions under which the transformed clauses have an 𝓐-definable modelif and only ifthe original ones have an 𝓐-definable model. Then, we present a strategy, called Predicate Pairing, which guides the application of the transformation rules with the objective of deriving a set of clauses whose satisfiability problem can be solved by looking for 𝓐-definable models. The Predicate Pairing (PP) strategy introduces a new predicate defined by the conjunction of two predicates occurring in the original set of clauses, together with a conjunction of constraints. We will show through some examples that an 𝓐-definable model may exist for the new predicate even if it does not exist for its defining atomic conjuncts. We will also present some case studies showing that Predicate Pairing plays a crucial role in the verification ofrelational properties of programs, that is, properties relating two programs (such as program equivalence) or two executions of the same program (such as non-interference). Finally, we perform an experimental evaluation of the proposed techniques to assess the effectiveness of Predicate Pairing in increasing the power of CHC solving.

Abstract Ion chemistry with temperature evolution in weakly ionized plasma is important in plasma-assisted combustion and plasma-assisted catalysis, fuel reforming, and material synthesis due to its contribution to plasma generation and state transition. In this study, the kinetic roles of ionic reactions in nanosecond discharge (NSD) plasma-assisted temperature-dependent decomposition and oxidation of methane are investigated by integrated studies of experimental measurements and mathematical simulations. A detailed plasma chemistry mechanism governing the decomposition and oxidation processes in a He/CH4/O2 combustible mixture is proposed and studied by including a set of electron impact reactions, reactions involving excited species, and ionic reactions. A zero-dimensional model incorporating the plasma kinetics solver ZDPlasKin and the combustion chemical kinetics solver CHEMKIN is used to calculate the time and temperature evolution of the ion density. Uncertainty analysis of ionic reactions on key species generation is conducted by using different referenced data, and insignificant sensitivity is found. The numerical model is consistent with experimental data for methane consumption and generation of major species including CO, CO2, and H2. By modeling the temporal evolution of key ions, it is observed that O2 + presents the largest concentration in the discharge stage, followed by CH4 +, CH3 +, and CH2 +, which is in accordance with the traditional ion chemistry in hydrocarbon flames and agrees well with molecular-beam mass spectrometer investigations. The path flux shows that the concentrations of key species, including electrons, O, OH, H, O(1D), O2(a1Δg), O2 +, CH3 +, and CH4 +, change within 1–2 orders of magnitude and that the transition from a homogeneous state to a contracted/constricted state does not occur. The path flux and sensitivity analysis reveal the significant roles of cations in the stimulation of active radical generation, including CH, O, OH, and O(1D), thus accelerating methane oxidation. This work provides a deep insight into the ion chemistry of temperature-dependent plasma-assisted CH4 oxidation.

A high-sensitivity plasmonic photonic crystal fiber (PCF) sensor is designed and a metal thin film is embedded for achieving surface plasmon resonance (SPR), which can detect the magnetic field and temperature simultaneously. Within the plasmonic PCF sensor, the SPR sensing is accomplished by coating both the upper sensing channel (Ch1) and the lower sensing channel (Ch2) with gold film. In addition, the temperature-sensitive medium polydimethylsiloxane (PDMS) is chosen to fill in Ch1, allowing the sensor to respond to the temperature. The magnetic field-sensitive medium magnetic fluid (MF) is chosen to fill in Ch2, allowing this sensor to respond to the magnetic field. During these processes, this proposed SPR-PCF sensor can achieve dual-parameter sensing. The paper also investigates the electrical field characteristics, structural parameters and sensing performance using COMSOL. Finally, under the magnetic field range of 50–130 Oe, this sensor has magnetic field sensing sensitivities of 0 pm/Oe (Ch1) and 235 pm/Oe (Ch2). In addition, this paper also investigates the response of temperature. Under the temperature range of 20–40 °C, Ch1 and Ch2 have temperature sensitivities of −2000 pm/°C and 0 pm/°C, respectively. It is noteworthy that the two sensing channels respond to only a single physical parameter; this sensing performance is not common in dual-parameter sensing. Due to this sensing performance, it can be found that the magnetic field and temperature can be detected by this designed SPR-PCF sensor simultaneously without founding and calculating a sensing matrix. This sensing performance can solve the cross-sensitivity problem of magnetic field and temperature, thus reducing the measurement error. Since it can sense without a matrix, it further can solve the ill-conditioned matrix and nonlinear change in sensitivity problems in dual-parameter sensing. These excellent sensing capabilities are very important for carrying out multiparameter sensing in complicated environments.

The state-of-the-art SAT solvers usually share the same core techniques, for instance: the watched literals structure, conflict clause recording and non-chronological backtracking. Nevertheless, they might differ in the elimination of learnt clauses, as well as in the decision heuristic. This article presents a framework for generating configurable SAT solvers. The proposed framework is composed of the following components: a Base SAT Solver, a Perl Preprocessor, XML files (Solver Description and Heuristics Description files) to describe each heuristic as well as the set of heuristics that the generated solver uses. This solvers may use several techniques and heuristics such as those implemented in BerkMin, and in Equivalence Checking of Dissimilar Circuits, and also in Minisat. In order to demonstrate the effectiveness of the proposed framework, this article also presents three distinct SAT solver instances generated by the framework to address a complex and challenging industry problem: the Combinational Equivalence Checking problem (CEC).The first instance is a SAT solver that uses BerkMin and Dissimilar Circuits core techniques except the learnt clause elimination heuristic that has been adapted from Minisat; the second is another solver that combines BerkMin and Minisat decision heuristics at run-time; and the third is yet another SAT solver that changes the database reducing heuristic at run-time. The experiments demonstrate that the first SAT solver generated is a faster solver than state-of-the-art SAT solver BerkMin for several instances as well as for Minisat in almost every instance.