Degeneralization Algorithm for Generation of Büchi Automata Based on Contented Situation

We present on-the-fly degeneralization algorithm used to transform generalized Büchi automata (GBA) into Büchi Automata (BA) different from the standard degeneralization algorithm. Contented situation, which is used to record what acceptance conditions are satisfiable during expanding LTL formulae, is attached to the states and transitions in the BA. In order to get the deterministic BA, the Shannon expansion is used recursively when we expand LTL formulae by applying the tableau rules. On-the-fly degeneralization algorithm is carried out in each step of the expansion of LTL formulae. Ordered binary decision diagrams are used to represent the BA and simplify LTL formulae. The temporary automata are stored as syntax directed acyclic graph in order to save storage space. These ideas are implemented in a conversion algorithm used to build a property automaton corresponding to the given LTL formulae. We compare our method to previous work and show that it is more efficient for four sets of random formulae generated by LBTT

Mightyl: A compositional translation from mitl to timed automata

Metric Interval Temporal Logic (MITL) was first proposed in the early 1990s as a specification formalism for real-time systems. Apart from its appealing intuitive syntax, there are also theoretical evidences that make MITL a prime real-time counterpart of Linear Temporal Logic (LTL). Unfortunately, the tool support for MITL verification is still lacking to this day. In this paper, we propose a new construction from MITL to timed automata via very-weak one-clock alternating timed automata. Our construction subsumes the well-known construction from LTL to Büchi automata by Gastin and Oddoux and yet has the additional benefits of being compositional and integrating easily with existing tools. We implement the construction in our new tool MightyL and report on experiments using Uppaal and LTSmin as back-ends

Constraint LTL Satisfiability Checking without Automata

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.Comment: 39 page

One Theorem to Rule Them All: A Unified Translation of LTL into {\omega}-Automata

We present a unified translation of LTL formulas into deterministic Rabin automata, limit-deterministic B\"uchi automata, and nondeterministic B\"uchi automata. The translations yield automata of asymptotically optimal size (double or single exponential, respectively). All three translations are derived from one single Master Theorem of purely logical nature. The Master Theorem decomposes the language of a formula into a positive boolean combination of languages that can be translated into {\omega}-automata by elementary means. In particular, Safra's, ranking, and breakpoint constructions used in other translations are not needed

starMC: an automata based CTL* model checker

Model-checking of temporal logic formulae is a widely used technique for the verification of systems. CTL [Image: see text] is a temporal logic that allows to consider an intermix of both branching behaviours (like in CTL) and linear behaviours (LTL), overcoming the limitations of LTL (that cannot express “possibility”) and CTL (cannot fully express fairness). Nevertheless CTL [Image: see text] model-checkers are uncommon. This paper presents (1) the algorithms for a fully symbolic automata-based approach for CTL [Image: see text] , and (2) their implementation in the open-source tool starMC, a CTL [Image: see text] model checker for systems specified as Petri nets. Testing has been conducted on thousands of formulas over almost a hundred models. The experiments show that the fully symbolic automata-based approach of starMC can compute the set of states that satisfy a CTL [Image: see text] formula for very large models (non trivial formulas for state spaces larger than 10(480) states are evaluated in less than a minute)

Specification and Verification using Temporal Logics

International audienceThis chapter illustrates two aspects of automata theory related to linear-time temporal logic LTL used for the verification of computer systems. First, we present a translation from LTL formulae to Büchi automata. The aim is to design an elementary translation which is reasonably efficient and produces small automata so that it can be easily taught and used by hand on real examples. Our translation is in the spirit of the classical tableau constructions but is optimized in several ways. Secondly, we recall how temporal operators can be defined from regular languages and we explain why adding even a single operator definable by a context-free language can lead to undecidability

Runtime Verification Using a Temporal Description Logic Revisited

Formulae of linear temporal logic (LTL) can be used to specify (wanted or unwanted) properties of a dynamical system. In model checking, the system’s behaviour is described by a transition system, and one needs to check whether all possible traces of this transition system satisfy the formula. In runtime verification, one observes the actual system behaviour, which at any point in time yields a finite prefix of a trace. The task is then to check whether all continuations of this prefix to a trace satisfy (violate) the formula. More precisely, one wants to construct a monitor, i.e., a finite automaton that receives the finite prefix as input and then gives the right answer based on the state currently reached. In this paper, we extend the known approaches to LTL runtime verification in two directions. First, instead of propositional LTL we use the more expressive temporal logic ALC-LTL, which can use axioms of the Description Logic (DL) ALC instead of propositional variables to describe properties of single states of the system. Second, instead of assuming that the observed system behaviour provides us with complete information about the states of the system, we assume that states are described in an incomplete way by ALC-knowledge bases. We show that also in this setting monitors can effectively be constructed. The (double-exponential) size of the constructed monitors is in fact optimal, and not higher than in the propositional case. As an auxiliary result, we show how to construct Büchi automata for ALC-LTL-formulae, which yields alternative proofs for the known upper bounds of deciding satisfiability in ALC-LTL

Complexity of Model Checking MDPs against LTL Specifications

Given a Markov Decision Process (MDP) M, an LTL formula varphi, and a threshold theta in [0,1], the verification question is to determine if there is a scheduler with respect to which the executions of M satisfying varphi have probability greater than (or greater than or equal to) theta. When theta = 0, we call it the qualitative verification problem, and when theta in (0,1], we call it the quantitative verification problem. In this paper we study the precise complexity of these problems when the specification is constrained to be in different fragments of LTL