Linear Encodings of Bounded LTL Model Checking

We consider the problem of bounded model checking (BMC) for linear temporal logic (LTL). We present several efficient encodings that have size linear in the bound. Furthermore, we show how the encodings can be extended to LTL with past operators (PLTL). The generalised encoding is still of linear size, but cannot detect minimal length counterexamples. By using the virtual unrolling technique minimal length counterexamples can be captured, however, the size of the encoding is quadratic in the specification. We also extend virtual unrolling to Buchi automata, enabling them to accept minimal length counterexamples. Our BMC encodings can be made incremental in order to benefit from incremental SAT technology. With fairly small modifications the incremental encoding can be further enhanced with a termination check, allowing us to prove properties with BMC. Experiments clearly show that our new encodings improve performance of BMC considerably, particularly in the case of the incremental encoding, and that they are very competitive for finding bugs. An analysis of the liveness-to-safety transformation reveals many similarities to the BMC encodings in this paper. Using the liveness-to-safety translation with BDD-based invariant checking results in an efficient method to find shortest counterexamples that complements the BMC-based approach.Comment: Final version for Logical Methods in Computer Science CAV 2005 special issu

SAT-based Explicit LTL Reasoning

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

Platform Dependent Verification: On Engineering Verification Tools for 21st Century

The paper overviews recent developments in platform-dependent explicit-state LTL model checking.Comment: In Proceedings PDMC 2011, arXiv:1111.006

Truly On-The-Fly LTL Model Checking

We propose a novel algorithm for automata-based LTL model checking that interleaves the construction of the generalized B\"{u}chi automaton for the negation of the formula and the emptiness check. Our algorithm first converts the LTL formula into a linear weak alternating automaton; configurations of the alternating automaton correspond to the locations of a generalized B\"{u}chi automaton, and a variant of Tarjan's algorithm is used to decide the existence of an accepting run of the product of the transition system and the automaton. Because we avoid an explicit construction of the B\"{u}chi automaton, our approach can yield significant improvements in runtime and memory, for large LTL formulas. The algorithm has been implemented within the SPIN model checker, and we present experimental results for some benchmark examples

Counterexample-Preserving Reduction for Symbolic Model Checking

The cost of LTL model checking is highly sensitive to the length of the formula under verification. We observe that, under some specific conditions, the input LTL formula can be reduced to an easier-to-handle one before model checking. In our reduction, these two formulae need not to be logically equivalent, but they share the same counterexample set w.r.t the model. In the case that the model is symbolically represented, the condition enabling such reduction can be detected with a lightweight effort (e.g., with SAT-solving). In this paper, we tentatively name such technique "Counterexample-Preserving Reduction" (CePRe for short), and finally the proposed technquie is experimentally evaluated by adapting NuSMV

Improving HyLTL model checking of hybrid systems

The problem of model-checking hybrid systems is a long-time challenge in the scientific community. Most of the existing approaches and tools are either limited on the properties that they can verify, or restricted to simplified classes of systems. To overcome those limitations, a temporal logic called HyLTL has been recently proposed. The model checking problem for this logic has been solved by translating the formula into an equivalent hybrid automaton, that can be analized using existing tools. The original construction employs a declarative procedure that generates exponentially many states upfront, and can be very inefficient when complex formulas are involved. In this paper we solve a technical issue in the construction that was not considered in previous works, and propose a new algorithm to translate HyLTL into hybrid automata, that exploits optimized techniques coming from the discrete LTL community to build smaller automata.Comment: In Proceedings GandALF 2013, arXiv:1307.416

Efficient Parallel Statistical Model Checking of Biochemical Networks

We consider the problem of verifying stochastic models of biochemical networks against behavioral properties expressed in temporal logic terms. Exact probabilistic verification approaches such as, for example, CSL/PCTL model checking, are undermined by a huge computational demand which rule them out for most real case studies. Less demanding approaches, such as statistical model checking, estimate the likelihood that a property is satisfied by sampling executions out of the stochastic model. We propose a methodology for efficiently estimating the likelihood that a LTL property P holds of a stochastic model of a biochemical network. As with other statistical verification techniques, the methodology we propose uses a stochastic simulation algorithm for generating execution samples, however there are three key aspects that improve the efficiency: first, the sample generation is driven by on-the-fly verification of P which results in optimal overall simulation time. Second, the confidence interval estimation for the probability of P to hold is based on an efficient variant of the Wilson method which ensures a faster convergence. Third, the whole methodology is designed according to a parallel fashion and a prototype software tool has been implemented that performs the sampling/verification process in parallel over an HPC architecture