Local Distributed Model Checking of Reg CTL

AbstractThe paper is devoted to the problem of extending the temporal logic CTL so that it is more expressive and complicated properties can be expressed more succinctly. The specification language Reg CTL, an extension of CTL, is proposed. In Reg CTL every CTL temporal operator is augmented with a regular expression restricting thus moments when the validity is required. The resulting logic is more expressive than previous extensions of CTL with regular expressions. Reg CTL can be model-checked on-the-fly and the model checking algorithm is well distributable

A Quantitative Extension of Interval Temporal Logic over Infinite Words

Model checking (MC) for Halpern and Shoham’s interval temporal logic HS has been recently investigated in a systematic way, and it is known to be decidable under three distinct semantics (state-based, trace-based and tree-based semantics), all of them assuming homogeneity in the propositional valuation. Here, we focus on the trace-based semantics, where the main semantic entities are the infinite execution paths (traces) of the given Kripke structure. We introduce a quantitative extension of HS over traces, called Difference HS (DHS), allowing one to express timing constraints on the difference among interval lengths (durations). We show that MC and satisfiability of full DHS are in general undecidable, so, we investigate the decidability border for these problems by considering natural syntactical fragments of DHS. In particular, we identify a maximal decidable fragment DHSsimple of DHS proving in addition that the considered problems for this fragment are at least 2Expspace-hard. Moreover, by exploiting new results on linear-time hybrid logics, we show that for an equally expressive fragment of DHSsimple, the problems are Expspace-complete. Finally, we provide a characterization of HS over traces by means of the one-variable fragment of a novel hybrid logic

Propositional Dynamic Logic for Hyperproperties

Information security properties of reactive systems like non-interference often require relating different executions of the system to each other and following them simultaneously. Such hyperproperties can also be useful in other contexts, e.g., when analysing properties of distributed systems like linearizability. Since common logics like LTL, CTL, or the modal ?-calculus cannot express hyperproperties, the hyperlogics HyperLTL and HyperCTL^* were developed to cure this defect. However, these logics are not able to express arbitrary ?-regular properties. In this paper, we introduce HyperPDL-?, an adaptation of the Propositional Dynamic Logic of Fischer and Ladner for hyperproperties, in order to remove this limitation. Using an elegant automata-theoretic framework, we show that HyperPDL-? model checking is asymptotically not more expensive than HyperCTL^* model checking, despite its vastly increased expressive power. We further investigate fragments of HyperPDL-? with regard to satisfiability checking

On regular temporal logics with past

The IEEE standardized Property Specification Language, PSL for short, extends the well-known linear-time temporal logic LTL with so-called semi-extended regular expressions. PSL and the closely related SystemVerilog Assertions, SVA for short, are increasingly used in many phases of the hardware design cycle, from specification to verification. In this article, we extend the common core of these specification languages with past operators. We name this extension PPSL. Although all ω-regular properties are expressible in PSL, SVA, and PPSL, past operators often allow one to specify properties more naturally and concisely. In fact, we show that PPSL is exponentially more succinct than the cores of PSL and SVA. On the star-free properties, PPSL is double exponentially more succinct than LTL. Furthermore, we present a translation of PPSL into language-equivalent nondeterministic Büchi automata, which is based on novel constructions for 2-way alternating automata. The upper bound on the size of the resulting nondeterministic Büchi automata obtained by our translation is almost the same as the upper bound for the nondeterministic Büchi automata obtained from existing translations for PSL and SVA. Consequently, the satisfiability problem and the model-checking problem for PPSL fall into the same complexity classes as the corresponding problems for PSL and SV

Partially ordered two-way Büchi automata

We introduce partially ordered two-way Büchi automata over infinite words. As for finite words, the nondeterministic variant recognizes the fragment Sigma2 of first-order logic FO[<] and the deterministic version yields the Delta2-definable omega-languages. As a byproduct of our results, we show that deterministic partially ordered two-way Büchi automata are effectively closed under Boolean operations. In addition, we have coNP-completeness results for the emptiness problem and the inclusion problem over deterministic partially ordered two-way Büchi automata

Extended Computation Tree Logic

We introduce a generic extension of the popular branching-time logic CTL which refines the temporal until and release operators with formal languages. For instance, a language may determine the moments along a path that an until property may be fulfilled. We consider several classes of languages leading to logics with different expressive power and complexity, whose importance is motivated by their use in model checking, synthesis, abstract interpretation, etc. We show that even with context-free languages on the until operator the logic still allows for polynomial time model-checking despite the significant increase in expressive power. This makes the logic a promising candidate for applications in verification. In addition, we analyse the complexity of satisfiability and compare the expressive power of these logics to CTL* and extensions of PDL

О задаче верификации моделей программ для одного расширения логики CTL*

Sequential reactive systems include programs and devices that work with two streams of data and convert input streams of data into output streams. Such information processing systems include controllers, device drivers, computer interpreters. The result of the operation of such computing systems are infinite sequences of pairs of events of the request-response type, and, therefore, finite transducers are most often used as formal models for them. The behavior of transducers is represented by binary relations on infinite sequences, and so, traditional applied temporal logics (like HML, LTL, CTL, mu-calculus) are poorly suited as specification languages, since omega-languages, not binary relations on omega-words are used for interpretation of their formulae. To provide temporal logics with the ability to define properties of transformations that characterize the behavior ofreactive systems, we introduced new extensions ofthese logics, which have two distinctive features: 1) temporal operators are parameterized, and languages in the input alphabet oftransducers are used as parameters; 2) languages in the output alphabet oftransducers are used as basic predicates. Previously, we studied the expressive power ofnew extensions Reg-LTL and Reg-CTL ofthe well-known temporal logics oflinear and branching time LTL and CTL, in which it was allowed to use only regular languages for parameterization of temporal operators and basic predicates. We discovered that such a parameterization increases the expressive capabilities oftemporal logic, but preserves the decidability of the model checking problem. For the logics mentioned above, we have developed algorithms for the verification of finite transducers. At the next stage of our research on the new extensions of temporal logic designed for the specification and verification of sequential reactive systems, we studied the verification problem for these systems using the temporal logic Reg-CTL*, which is an extension ofthe Generalized Computational Tree Logics CTL*. In this paper we present an algorithm for checking the satisfiability of Reg-CTL* formulae on models of finite state transducers and show that this problem belongs to the complexity class ExpSpace.К последовательным реагирующим системам относятся программы и устройства, которые работают с двумя потоками данных и осуществляют преобразование входных потоков данных в выходные потоки. К числу таких систем обработки информации относятся контроллеры, драйверы устройств, компьютерные интерпретаторы. Результатом работы таких вычислительных систем являются бесконечные последовательности пар событий типа запрос-отклик, и поэтому в качестве математических моделей для них наиболее часто используются конечные автоматы-преобразователи. Поведение автоматов-преобразователей представлено бинарными отношениями на бесконечных последовательностях, и традиционные прикладные темпоральные логики (HML, LTL, CTL, mu-исчисление) плохо подходят для этой цели, поскольку для интерпретации их формул используются omega-языки, а не бинарные отношения на omega-словах. Чтобы предоставить темпоральным логикам возможность определять свойства преобразований, которые характеризуют поведение реагирующих систем, мы ввели новые расширения этих логик, имеющие две отличительные особенности: 1) темпоральные операторы в расширениях этих логик параметризованы, и в качестве параметров используются языки в входном алфавите автоматов-преобразователей; 2) в качестве базовых предикатов используются языки в выходном алфавите автоматов-преобразователей. Ранее нами были исследованы выразительные возможности новых расширений Reg-LTL и Reg-CTL известных темпоральных логик линейного и ветвящегося времени LTL и CTL, в которых для параметризации темпоральных операторов и задания базовых предикатов разрешалось использовать только регулярные языки. Мы обнаружили, что такая параметризация увеличивает выразительные возможности темпоральной логики, но сохраняет разрешимость задачи проверки выполнимости формул на конечных моделях. Для указанных выше логик нами были разработаны алгоритмы верификации конечных автоматов-преобразователей. На следующем этапе изучения новых расширений темпоральной логики, предназначенных для спецификации и верификации последовательных реагирующих систем, мы обратились к задаче верификации этих систем с использованием темпоральной логики Reg-CTL*, которая является расширением обобщенной логики деревьев вычислений CTL*. В этой статье описан алгоритм проверки выполнимости формул Reg-CTL* на моделях конечных автоматов-преобразователей и показано, что эта задача принадлежит классу сложности ExpSpace

On the Satisfiability and Model Checking for one Parameterized Extension of Linear-time Temporal Logic

Sequential reactive systems are computer programs or hardware devices which process the flows of input data or control signals and output the streams of instructions or responses. When designing such systems one needs formal specification languages capable of expressing the relationships between the input and output flows. Previously, we introduced a family of such specification languages based on temporal logics $LTL$, $CTL$ and $CTL^*$ combined with regular languages. A characteristic feature of these new extensions of conventional temporal logics is that temporal operators and basic predicates are parameterized by regular languages. In our early papers, we estimated the expressive power of the new temporal logic $Reg$-$LTL$ and introduced a model checking algorithm for $Reg$-$LTL$, $Reg$-$CTL$, and $Reg$-$CTL^*$. The main issue which still remains unclear is the complexity of decision problems for these logics. In the paper, we give a complete solution to satisfiability checking and model checking problems for $Reg$-$LTL$ and prove that both problems are Pspace-complete. The computational hardness of the problems under consideration is easily proved by reducing to them the intersection emptyness problem for the families of regular languages. The main result of the paper is an algorithm for reducing the satisfiability of checking $Reg$-$LTL$ formulas to the emptiness problem for Buchi automata of relatively small size and a description of a technique that allows one to check the emptiness of the obtained automata within space polynomial of the size of input formulas