Efficient Parallel Path Checking for Linear-Time Temporal Logic With Past and Bounds

Path checking, the special case of the model checking problem where the model under consideration is a single path, plays an important role in monitoring, testing, and verification. We prove that for linear-time temporal logic (LTL), path checking can be efficiently parallelized. In addition to the core logic, we consider the extensions of LTL with bounded-future (BLTL) and past-time (LTL+Past) operators. Even though both extensions improve the succinctness of the logic exponentially, path checking remains efficiently parallelizable: Our algorithm for LTL, LTL+Past, and BLTL+Past is in AC^1(logDCFL) \subseteq NC

Fast LTL Satisfiability Checking by SAT Solvers

Satisfiability checking for Linear Temporal Logic (LTL) is a fundamental step in checking for possible errors in LTL assertions. Extant LTL satisfiability checkers use a variety of different search procedures. With the sole exception of LTL satisfiability checking based on bounded model checking, which does not provide a complete decision procedure, LTL satisfiability checkers have not taken advantage of the remarkable progress over the past 20 years in Boolean satisfiability solving. In this paper, we propose a new LTL satisfiability-checking framework that is accelerated using a Boolean SAT solver. Our approach is based on the variant of the \emph{obligation-set method}, which we proposed in earlier work. We describe here heuristics that allow the use of a Boolean SAT solver to analyze the obligations for a given LTL formula. The experimental evaluation indicates that the new approach provides a a significant performance advantage

Parametric Linear Dynamic Logic

We introduce Parametric Linear Dynamic Logic (PLDL), which extends Linear Dynamic Logic (LDL) by temporal operators equipped with parameters that bound their scope. LDL was proposed as an extension of Linear Temporal Logic (LTL) that is able to express all $\omega$-regular specifications while still maintaining many of LTL's desirable properties like an intuitive syntax and a translation into non-deterministic B\"uchi automata of exponential size. But LDL lacks capabilities to express timing constraints. By adding parameterized operators to LDL, we obtain a logic that is able to express all $\omega$-regular properties and that subsumes parameterized extensions of LTL like Parametric LTL and PROMPT-LTL. Our main technical contribution is a translation of PLDL formulas into non-deterministic B\"uchi word automata of exponential size via alternating automata. This yields a PSPACE model checking algorithm and a realizability algorithm with doubly-exponential running time. Furthermore, we give tight upper and lower bounds on optimal parameter values for both problems. These results show that PLDL model checking and realizability are not harder than LTL model checking and realizability.Comment: In Proceedings GandALF 2014, arXiv:1408.556

Abstraction-Based Model Checking of Linear Temporal Properties

Even though the expressiveness of linear temporal logic (LTL) supports engineering application, model checking of such properties is a computationally complex task and state space explosion often hinders successful verification. LTL model checking consists of constructing automata from the property and the system, generating the synchronous product of the two automata and checking its language emptiness. We propose a novel LTL model checking algorithm that uses abstraction to tackle the challenge of state space explosion. This algorithm combines the advantages of two commonly used model checking approaches, counterexample-guided abstraction refinement and automata theoretic LTL model checking. The main challenge in combining these is the refinement of "lasso"-shaped counterexamples, for which task we propose a novel refinement strategy based on interpolation

Parameterized Linear Temporal Logics Meet Costs: Still not Costlier than LTL

We continue the investigation of parameterized extensions of Linear Temporal Logic (LTL) that retain the attractive algorithmic properties of LTL: a polynomial space model checking algorithm and a doubly-exponential time algorithm for solving games. Alur et al. and Kupferman et al. showed that this is the case for Parametric LTL (PLTL) and PROMPT-LTL respectively, which have temporal operators equipped with variables that bound their scope in time. Later, this was also shown to be true for Parametric LDL (PLDL), which extends PLTL to be able to express all omega-regular properties. Here, we generalize PLTL to systems with costs, i.e., we do not bound the scope of operators in time, but bound the scope in terms of the cost accumulated during time. Again, we show that model checking and solving games for specifications in PLTL with costs is not harder than the corresponding problems for LTL. Finally, we discuss PLDL with costs and extensions to multiple cost functions.Comment: In Proceedings GandALF 2015, arXiv:1509.0685

DiVinE-CUDA - A Tool for GPU Accelerated LTL Model Checking

In this paper we present a tool that performs CUDA accelerated LTL Model Checking. The tool exploits parallel algorithm MAP adjusted to the NVIDIA CUDA architecture in order to efficiently detect the presence of accepting cycles in a directed graph. Accepting cycle detection is the core algorithmic procedure in automata-based LTL Model Checking. We demonstrate that the tool outperforms non-accelerated version of the algorithm and we discuss where the limits of the tool are and what we intend to do in the future to avoid them

Bounded LTL Model Checking with Stable Models

In this paper bounded model checking of asynchronous concurrent systems is introduced as a promising application area for answer set programming. As the model of asynchronous systems a generalisation of communicating automata, 1-safe Petri nets, are used. It is shown how a 1-safe Petri net and a requirement on the behaviour of the net can be translated into a logic program such that the bounded model checking problem for the net can be solved by computing stable models of the corresponding program. The use of the stable model semantics leads to compact encodings of bounded reachability and deadlock detection tasks as well as the more general problem of bounded model checking of linear temporal logic. Correctness proofs of the devised translations are given, and some experimental results using the translation and the Smodels system are presented.Comment: 32 pages, to appear in Theory and Practice of Logic Programmin