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Constraint LTL Satisfiability Checking without Automata  [PDF]
Marcello M. Bersani,Achille Frigeri,Angelo Morzenti,Matteo Pradella,Matteo Rossi,Pierluigi San Pietro
Computer Science , 2012,
Abstract: This paper introduces a novel technique to decide the satisfiability of formulae written in the language of Linear Temporal Logic with Both future and past operators and atomic formulae belonging to constraint system D (CLTLB(D) for short). The technique is based on the concept of bounded satisfiability, and hinges on an encoding of CLTLB(D) formulae into QF-EUD, the theory of quantifier-free equality and uninterpreted functions combined with D. Similarly to standard LTL, where bounded model-checking and SAT-solvers can be used as an alternative to automata-theoretic approaches to model-checking, our approach allows users to solve the satisfiability problem for CLTLB(D) formulae through SMT-solving techniques, rather than by checking the emptiness of the language of a suitable automaton A_{\phi}. The technique is effective, and it has been implemented in our Zot formal verification tool.
Variable and clause elimination for LTL satisfiability checking  [PDF]
Martin Suda
Computer Science , 2013,
Abstract: We study preprocessing techniques for clause normal forms of LTL formulas. Applying the mechanism of labelled clauses enables us to reinterpret LTL satisfiability as a set of purely propositional problems and thus to transfer simplification ideas from SAT to LTL. We demonstrate this by adapting variable and clause elimination, a very effective preprocessing technique used by modern SAT solvers. Our experiments confirm that even in the temporal setting substantial reductions in formula size and subsequent decrease of solver runtime can be achieved.
Polsat: A Portfolio LTL Satisfiability Solver  [PDF]
Jianwen Li,Geguang Pu,Lijun Zhang,Yinbo Yao,Moshe Y. Vardi,Jifeng he
Computer Science , 2013,
Abstract: In this paper we present a portfolio LTL-satisfiability solver, called Polsat. To achieve fast satisfiability checking for LTL formulas, the tool integrates four representative LTL solvers: pltl, TRP++, NuSMV, and Aalta. The idea of Polsat is to run the component solvers in parallel to get best overall performance; once one of the solvers terminates, it stops all other solvers. Remarkably, the Polsat solver utilizes the power of modern multi-core compute clusters. The empirical experiments show that Polsat takes advantages of it. Further, Polsat is also a testing plat- form for all LTL solvers.
LTLf satisfiability checking  [PDF]
Jianwen Li,Lijun Zhang,Geguang Pu,Moshe Y. Vardi,Jifeng He
Computer Science , 2014,
Abstract: We consider here Linear Temporal Logic (LTL) formulas interpreted over \emph{finite} traces. We denote this logic by LTLf. The existing approach for LTLf satisfiability checking is based on a reduction to standard LTL satisfiability checking. We describe here a novel direct approach to LTLf satisfiability checking, where we take advantage of the difference in the semantics between LTL and LTLf. While LTL satisfiability checking requires finding a \emph{fair cycle} in an appropriate transition system, here we need to search only for a finite trace. This enables us to introduce specialized heuristics, where we also exploit recent progress in Boolean SAT solving. We have implemented our approach in a prototype tool and experiments show that our approach outperforms existing approaches.
SAT-based Explicit LTL Reasoning  [PDF]
Jianwen Li,Shufang Zhu,Geguang Pu,Moshe Vardi
Computer Science , 2015,
Abstract: We present here a new explicit reasoning framework for linear temporal logic (LTL), which is built on top of propositional satisfiability (SAT) solving. As a proof-of-concept of this framework, we describe a new LTL satisfiability tool, Aalta\_v2.0, which is built on top of the MiniSAT SAT solver. We test the effectiveness of this approach by demonnstrating that Aalta\_v2.0 significantly outperforms all existing LTL satisfiability solvers. Furthermore, we show that the framework can be extended from propositional LTL to assertional LTL (where we allow theory atoms), by replacing MiniSAT with the Z3 SMT solver, and demonstrating that this can yield an exponential improvement in performance.
Checking Satisfiability by Dependency Sequents  [PDF]
Eugene Goldberg,Panagiotis Manolios
Computer Science , 2012,
Abstract: We introduce a new algorithm for checking satisfiability based on a calculus of Dependency sequents (D-sequents). Given a CNF formula F(X), a D-sequent is a record stating that under a partial assignment a set of variables of X is redundant in formula \exists{X}[F]. The D-sequent calculus is based on operation join that forms a new D-sequent from two existing D-sequents. The new algorithm solves the quantified version of SAT. That is, given a satisfiable formula F, it, in general, does not produce an assignment satisfying F. The new algorithm is called DS-QSAT where DS stands for Dependency Sequent and Q for Quantified. Importantly, a DPLL-like procedure is only a special case of DS-QSAT where a very restricted kind of D-sequents is used. We argue that this restriction a) adversely affects scalability of SAT-solvers and b) is caused by looking for an explicit satisfying assignment rather than just proving satisfiability. We give experimental results substantiating these claims.
Space-Efficient Bounded Model Checking  [PDF]
Jacob Katz,Ziyad Hanna,Nachum Dershowitz
Computer Science , 2007, DOI: 10.1109/DATE.2005.276
Abstract: Current algorithms for bounded model checking use SAT methods for checking satisfiability of Boolean formulae. These methods suffer from the potential memory explosion problem. Methods based on the validity of Quantified Boolean Formulae (QBF) allow an exponentially more succinct representation of formulae to be checked, because no "unrolling" of the transition relation is required. These methods have not been widely used, because of the lack of an efficient decision procedure for QBF. We evaluate the usage of QBF in bounded model checking (BMC), using general-purpose SAT and QBF solvers. We develop a special-purpose decision procedure for QBF used in BMC, and compare our technique with the methods using general-purpose SAT and QBF solvers on real-life industrial benchmarks.
Improved SMT-Based Bounded Model Checking for Real-Time Systems
改进的以SMT为基础的实时系统限界模型检测

XU Liang,
徐亮

计算机系统应用 , 2010,
Abstract: SAT-Based bounded model checking (BMC) has high complexity in dealing with real-time systems. Satisfiability modulo theories (SMT) solvers can generalize SAT solving by adding the ability to handle arithmetic and other decidable theories. This paper uses SMT in BMC for real-time systems instead of SAT. The clocks can be represented as integer or real variables directly and clock constraints can be represented as linear arithmetic expressions. These make the checking procedure more efficient. TCTL (timed computation tree logic) is used to specify the properties of real-time systems and improvement of the encodings has been done.
Improved SMT-Based Bounded Model Checking for Real-Time Systems
改进的以SMT为基础的实时系统限界模型检测

XU Liang,
徐亮

软件学报 , 2010,
Abstract: SAT-Based bounded model checking (BMC) has high complexity in dealing with real-time systems. Satisfiability modulo theories (SMT) solvers can generalize SAT solving by adding the ability to handle arithmetic and other decidable theories. This paper uses SMT in BMC for real-time systems instead of SAT. The clocks can be represented as integer or real variables directly and clock constraints can be represented as linear arithmetic expressions. These make the checking procedure more efficient. TCTL (timed computation tree logic) is used to specify the properties of real-time systems and improvement of the encodings has been done.
Implementing Efficient All Solutions SAT Solvers  [PDF]
Takahisa Toda,Takehide Soh
Computer Science , 2015,
Abstract: All solutions SAT (AllSAT for short) is a variant of propositional satisfiability problem. Despite its significance, AllSAT has been relatively unexplored compared to other variants. We thus survey and discuss major techniques of AllSAT solvers. We faithfully implement them and conduct comprehensive experiments using a large number of instances and various types of solvers including one of the few public softwares. The experiments reveal solver's characteristics. Our implemented solvers are made publicly available so that other researchers can easily develop their solver by modifying our codes and compare it with existing methods.
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