Constructing Automata from Temporal Logic Formulas: A Tutorial⋆ (original) (raw)

An automata-theoretic approach to linear temporal logic

Logics for concurrency, 1996

The automata-theoretic approach to linear temporal logic uses the theory of automata as a unifying paradigm for program specification, verification, and synthesis. Both programs and specifications are in essence descriptions of computations. These computations can be viewed as words over some alphabet. Thus, programs and specifications can be viewed as descriptions of languages over some alphabet. The automata-theoretic perspective considers the relationships between programs and their specifications as relationships between languages. By translating programs and specifications to automata, questions about programs and their specifications can be reduced to questions about automata. More specifically, questions such as satisfiability of specifications and correctness of programs with respect to their specifications can be reduced to questions such as nonemptiness and containment of automata. Unlike classical automata theory, which focused on automata on finite words, the applications to program specification, verification, and synthesis, use automata on infinite words, since the computations in which we are interested are typically infinite. This paper provides an introduction to the theory of automata on infinite words and demonstrates its applications to program specification, verification, and synthesis.

Improved Automata Generation for Linear Temporal Logic

Lecture Notes in Computer Science, 1999

We improve the state-of-the-art algorithm for obtaining an automaton from a linear temporal logic formula. The automaton is intended to be used for model checking, as well as for satisfiability checking. Therefore, the algorithm is mainly concerned with keeping the automaton as small as possible. The experimental results show that our algorithm outperforms the previous one, with respect to both the size of the generated automata and computation time. The testing is performed following a newly developed methodology based on the use of randomly generated formulas.

On-the-fly automata construction for dynamic linear time temporal logic

Proceedings. 11th International Symposium on Temporal Representation and Reasoning, 2004. TIME 2004., 2004

We present a tableau-based algorithm for obtaining a Büchi automaton from a formula in Dynamic Linear Time Temporal Logic (DLT L), a logic which extends LTL by indexing the until operator with regular programs. The construction of the states of the automaton is similar to the standard construction for LT L, but a different technique must be used to verify the fulfillment of until formulas. The resulting automaton is a Büchi automaton rather than a generalized one. The construction can be done on-the-fly, while checking for the emptiness of the automaton.

Tableau-based automata construction for dynamic linear time temporal logic*

Annals of Mathematics and Artificial Intelligence, 2006

We present a tableau-based algorithm for obtaining a Büchi automaton from a formula in Dynamic Linear Time Temporal Logic (DLTL), a logic which extends LTL by indexing the until operator with regular programs. The construction of the states of the automaton is similar to the standard construction for LTL, but a different technique must be used to verify the fulfillment of until formulas. The resulting automaton is a Büchi automaton rather than a generalized one. The construction can be done on-the-fly, while checking for the emptiness of the automaton. We also extend the construction to the Product Version of DLTL.

From Timed Automata to Logic - and Back

BRICS Report Series, 1995

One of the most successful techniques for automatic verification is that of model checking. For finite automata there exist since long extremely efficient model-checking algorithms, and in the last few years these algorithms have been made applicable to the verification of real-time automata using the region-techniques of Alur and Dill. In this paper, we continue this transfer of existing techniques from the setting of finite (untimed) automata to that of timed automata. In particular, a timed logic L ν is put forward, which is sufficiently expressive that we for any timed automaton may construct a single characteristic L ν formula uniquely characterizing the automaton up to timed bisimilarity. Also, we prove decidability of the satisfiability problem for L ν with respect to given bounds on the number of clocks and constants of the timed automata to be constructed. None of these results have as yet been succesfully accounted for in the presence of time 1. * This work has been supported by the European Communities under CONCUR2, BRA 7166 † Basic Research in Computer Science, Centre of the Danish National Research Foundation. 1 An exception occurs in Alur's thesis [Alu91] in which a decidability result is presented for a linear timed logic called MITL.

The Influence of Temporal Logic on Finite Automata

Al-Rafidain Engineering Journal (AREJ)

The theory of automata combines ideas from engineering, linguistics, mathematics, philosophy, etc. The Entscheidungsproblem asks if it is possible to design a series of steps that replaces a mathematician. An automaton is an abstract machine that processes data. C. Shannon's theory is today's most popular despite having no relationship with the other. The Kt system is called "minimal" because it makes no assumptions about the structure of time. In LKt, we have four monary temporal operators, F, P, G and H, which are mutually interdefinable. Interdefinability means that we will pass logic in the future is the same as saying I will never fail logic, interpreting not passing logic as failing logic. The minimal system syntax of temporal logic introduces operators that have the property of being defined in terms of others. Modal logic studies the reasoning that involves the use of expressions "necessarily" and "possibly". In this article, we will represent through a finite automaton the temporal logic formula Fp. It allows us to see an acceptance pattern for Fp by considering two variables: p and q. Kt's axiomatic system of time expresses the idea that both the present and the past are fixed, if it has always been in the past that it will be some time in the future that p is now. No philosophical argument supports deterministic time flow; the logic of time must be open.Temporal logic has revived many old problems, from the Megaric-Stoics to the minimal system of temporal logic. Our work suggests that the future operators of system Kt follow an evaluation pattern, but we must be cautious because this pattern can only apply to models whose time flow is based on instants and precedence relations.

Alternating automata: Unifying truth and validity checking for temporal logics

1997

We describe an automata-theoretic approach to the automated checking of truth and validity for temporal logics. The basic idea underlying this approach is that for any formula we can construct an alternating automaton that accepts precisely the models of the formula. For linear temporal logics the automaton runs on infinite words while for branching temporal logics the automaton runs on infinite trees.

Automata: from logics to algorithms

2007

Abstract We review, in a unified framework, translations from five different logics—monadic second-order logic of one and two successors (S1S and S2S), linear-time temporal logic (LTL), computation tree logic (CTL), and modal µ-calculus (MC)—into appropriate models of finite-state automata on infinite words or infinite trees. Together with emptiness-testing algorithms for these models of automata, this yields decision procedures for these logics.

Towards an automata-theoretic counterpart of combined temporal logics

2001

In this paper, we define a new class of combined automata, called temporalized automata, which can be viewed as the automata-theoretic counterpart of temporalized logics, and show that relevant properties, such as closure under Boolean operations, decidability, and expressive equivalence with respect to temporal logics, transfer from component automata to temporalized ones. Furthermore, we successfully apply temporalized automata to provide the full secondorder theory of k-refinable downward unbounded layered structures with a temporal logic counterpart. Finally, we show how temporalized automata can be used to deal with relevant classes of reactive systems, such as granular reactive systems and mobile reactive systems.

From Mtl to Deterministic Timed Automata

Lecture Notes in Computer Science, 2010

In this paper we propose a novel technique for constructing timed automata from properties expressed in the logic MTL, under bounded-variability assumptions. We handle full MTL and in particular do not impose bounds on the future temporal connectives. Our construction is based on separation of the continuous time monitoring of the input sequence and discrete predictions regarding the future. The separation of the continuous from the discrete allows us to further determinize our automata. This leads, for the first time, to a construction from full MTL to deterministic timed automata.