Relating Linear and Branching Model Checking

In temporal-logic model checking, we verify the correctness of a program with respect to a desired behavior by checking whether a structure that models the program satisfies a temporal-logic formula that specifies the behavior. The model-checking problem for the branching-time temporal logic CTL can be solved in linear running time, and model-checking tools for CTL are used successfully in industrial applications. The development of programs that must meet rigid real-time constraints has brought with it a need for real-time temporal logics that enable quantitative reference to time. Early research on real-time temporal logics uses the discrete domain of the integers to model time. Present research on real-time temporal logics focuses on continuous time and uses the dense domain of the reals to model time. There, model checking becomes significantly more complicated. For example, the model-checking problem for TCTL, a continuous-time extension of the logic CTL, is PSPACE-complete.In this paper we suggest a reduction from TCTL model checking to CTL model checking. The contribution of such a reduction is twofold. Theoretically, while it has long been known that model-checking methods for untimed temporal logics can be extended quite easily to handle discrete time, it was not clear whether and how untimed methods can handle the reset quantifier of TCTL, which resets a realvalued clock. Practically, our reduction enables anyone who has a tool for CTL model checking to use it for TCTL model checking. The TCTL model-checking algorithm that follows from our reduction is in PSPACE, matching the known bound for this problem. In addition, it enjoys the wide distribution of CTL model-checking tools and the extensive and fruitful research efforts and heuristics that have been put into these tools.KeywordsModel CheckTemporal LogicAtomic PropositionKripke StructureTemporal ReasoningThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Different directions in parallel and distributed model checking: (invited talk)

Game Over: The Foci Approach to LTL Satisfiability and Model Checking

Model checking memoryful linear-time logics over one-counter automata

Model checking is emerging as a popular technology for reasoning about behavioral properties of a wide variety of software artifacts including: requirements models, architectural descriptions, designs, implementations, and process models. The complexity of model checking is well-known, yet cost-effective analyses have been achieved by exploiting, for example, naturally occurring abstractions and semantic properties of a target software artifact. semantic properties of target software artifacts. Adapting a model checking tool to exploit this kind of domain knowledge often requires in-depth knowledge of the tool's implementation.We believe that with appropriate tool support, domain experts will be able to develop efficient model checking-based analyses for a variety of software-related models. To explore this hypothesis, we have developed Bogor, a model checking framework with an extensible input language for defining domain-specific constructs and a modular interface design to ease the optimization of domain-specific state-space encodings, reductions and search algorithms. We present the pattern-oriented design of Bogor and discuss our experiences adapting it to efficiently model check Java programs and event-driven component-based designs.

The introduction of Past Operators enables to produce more natural formulation of a wide class of properties of reactive systems, compared to traditional pure future temporal logics. For this reason, past temporal logics are gaining increasing interest in several application areas, ranging from Requirement Engineering to Formal Verification and Model Checking. We show how SAT-based Bounded Model Checking techniques can be extended to deal with Linear Temporal Logics with Past Operators (PLTL). Though apparently simple, this task turns out to be absolutely non-trivial when tackled in its full generality. We discuss a bounded semantics for PLTL, we show that it is correct (and complete), and propose an encoding scheme able to cope with PLTL formulas. Finally, we implement the encoding in NuSMV, and present a first experimental evaluation of the approach.

For every finite model M and an LTL property ϕ, there exists a number $\mathcal{CT}$ (the Completeness Threshold) such that if there is no counterexample to ϕ in M of length $\mathcal{CT}$ or less, then M⊧ϕ. Finding this number, if it is sufficiently small, offers a practical method for making Bounded Model Checking complete. We describe how to compute an over-approximation to $\mathcal{CT}$ for a general LTL property using Büchi automata, following the Vardi-Wolper LTL model checking framework. Based on the value of $\mathcal{CT}$ , we prove that the complexity of standard SAT-based BMC is doubly exponential, and that consequently there is a complexity gap of an exponent between this procedure and standard LTL model checking. We discuss ways to bridge this gap. The article mainly focuses on observations regarding bounded model checking rather than on a presentation of new techniques.

Security protocols ensure secure communication between and within systems such as internet services, factories, and smartphones. As evidenced by numerous successful attacks against popular protocols such as TLS, designing protocols securely is a tedious and error-prone task. Model checkers greatly aid protocol verification, yet any single model checker is oftentimes insufficient to check a protocol's security in full. Instead, engineers are forced to maintain multiple overlapping and hopefully non-contradicting and non-diverging specifications, one per model-checking tool---an error-prone task.To address this problem, this paper presents VICE, a scenario-based approach to security-protocol verification. It provides a visual modeling language based for specifying security protocols independent of the model checker. It then automatically transforms the relevant fragments of these models into equivalent inputs to multiple model checkers. In result, VICE completely relieves the security engineer from choosing and specifying queries via a fully automatic generation of all necessary queries.Through a case study involving real-world specifications of eight security protocols, we show that VICE is applicable in practice.

Based on the Kripke structure, linear temporal logic and generalized possibility measure, this article studies the model checking problems of generalized possibilistic fuzzy linear temporal logic (GPoFTL). The generalized possibilistic Kripke structure is introduced to describe the system model. The syntax of GPoFTL, which includes fuzzy temporal operators such as ``soon'', ``presently'', ``gradually'', ``within'', ``last'', ``nearly always'', ``almost alwayss'', ``in the long distant future'', ``in the middle of'', ``nearly until'' and ``almost until'', and its language semantics and path semantics under generalized possibility measure are given. Next, we explain the semantics of fuzzy temporal operators through some examples and prove that GPoFTL is an extension of generalized possibilistic linear temporal logic in fuzzy time temporal logic. Furthermore, the GPoFTL model checking algorithm is given by explicit calculation formulas one by one for any GPoFTL formula involving fuzzy temporal operators using fuzzy matrix operations. Last, the algorithm of necessary threshold model checking of GPoFTL is studied using automata theory and its time complexity is discussed.

The two central decision problems that arise during the design of safety critical systems are the satisfiability and the model checking problem. While model checking can only be applied after implementing the system, satisfiability checking answers the question whether a system that satisfies the specification exists. Model checking is traditionally considered to be the simpler problem --- for branching-time and fixed point logics such as CTL, CTL*, ATL, and the classical and alternating time μ-calculus, the complexity of satisfiability checking is considerably higher than the model checking complexity. We show that ATL* is a notable exception of this rule: Both ATL* model checking and ATL* satisfiability checking are 2EXPTIME-complete.

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.

In formal verification, reliable results are of utmost importance. In model checking of digital systems, mainly incorrect implementations of the model checking algorithms due to logical errors are the source of wrong results. In probabilistic model checking, however, numerical instabilities are an additional source for inconsistent results. We motivate our investigations with an example, for which several state-of-the-art probabilistic model checking tools give completely wrong results due to inexact computations. We then analyze, at which points inaccuracies are introduced during the model checking process. We discuss first ideas how, in spite of these inaccuracies, reliable results can be obtained or at least the user be warned about potential correctness problems: (1) usage of exact (rational) arithmetic, (2) usage of interval arithmetic to obtain safe approximations of the actual probabilities, (3) provision of certificates which testify that the result is correct, and (4) integration of a "degree of belief" for each sub-formula into existing model checking tools.

We present the first approach to model checking for nonlinear analog systems. Based on digital CTL model checking ideas, results in hybrid model checking and special needs in analog verification, a new model checking tool has been implemented Published model checking tools for hybrid systems require discrete or partly linear system descriptions. Our focus is on nonlinear analog behavior, therefore a new approach is necessary. There are mainly two aspects to be considered. Firstly, a discrete model retaining the essential nonlinear analog behavior has to be developed Secondly, model checking for analog systems requires extensions of the language to define analog system properties in a reasonable way.

In the automata theoretic approach to explicit state LTL model checking, the synchronized product of the model and an automaton that represents the negated formula is checked for emptiness. In practice, a (transition-based generalized) Büchi automaton (TGBA) is used for this procedure. This paper investigates whether using a more general form of acceptance, namely a transition-based generalized Rabin automaton (TGRA), improves the model checking procedure. TGRAs can have significantly fewer states than TGBAs; however, the corresponding emptiness checking procedure is more involved. With recent advances in probabilistic model checking and LTL to TGRA translators, it is only natural to ask whether checking a TGRA directly is more advantageous in practice. We designed a multi-core TGRA checking algorithm and performed experiments on a subset of the models and formulas from the 2015 Model Checking Contest and generated LTL formulas for models from the BEEM database. While we found little to no improvement by checking TGRAs directly, we show how various aspects of a TGRA’s structure influences the model checking performance. In this paper, we also introduce a Fin-less acceptance condition, which is a disjunction of TGBAs. We show how to convert TGRAs into automata with Fin-less acceptance and show how a TGBA emptiness procedure can be extended to check Fin-less automata.

Model checking LTL with regular valuations for pushdown systems