This paper is a survey on logical aspects of finite automata. Central points are the connection between finite automata and monadic second-order logic, the Ehrenfeucht-Fraiss'e technique in the context of formal language theory, finite automata on !-words and their determinization, and a self-contained proof of the "Rabin Tree Theorem". Sections 5 and 6 contain material presented in a lecture series to the "Final Winter School of AMICS" (Palermo, February 1996). A modified version of the paper will be a chapter of the "Handbook of Formal Language Theory", edited by G. Rozenberg and A. Salomaa, to appear in Springer-Verlag. Keywords: Finite automata, monadic second-order logic, first-order logic, regular languages, star-free languages, tree automata, Ehrenfeucht-Fraiss'e game, !-automata, temporal logic, Buchi automata, Rabin tree automata, determinacy, decidable theories. Contents 1 Introduction 1 2 Models and Formulas 2 2.1 Words, Trees, and Graphs as Models . . . . . . . . . . ....

. Monadic second order logic (MSOL) over transition systems is considered. It is shown that every formula of MSOL which does not distinguish between bisimilar models is equivalent to a formula of the propositional -calculus. This expressive completeness result implies that every logic over transition systems invariant under bisimulation and translatable into MSOL can be also translated into the -calculus. This gives a precise meaning to the statement that most propositional logics of programs can be translated into the -calculus. 1 Introduction Transition systems are structures consisting of a nonempty set of states, a set of unary relations describing properties of states and a set of binary relations describing transitions between states. It was advocated by many authors [26, 3] that this kind of structures provide a good framework for describing behaviour of programs (or program schemes), or even more generally, engineering systems, provided their evolution in time is disc...

This paper presents a novel method to derive a Petri net from any specification model that can be mapped into a state-based representation with arcs labeled with symbols from an alphabet of events (a Transition System, TS). The method is based on the theory of regions for Elementary Transition Systems (ETS). Previous work has shown that for any ETS there exists a Petri net with minimum transition count (one transition for each label) with a reachability graph isomorphic to the original Transition System. The method makes use of the following three mechanisms, providing a framework for synthesis of safe Petri nets from arbitrary TSs. Firstly, the requirement of isomorphism is relaxed to a "more behavioural" form of equivalence, bisimulation of TSs, thus extending the class of synthesizable TSs to a new class called Excitation-Closed Transition Systems(ECTS). Secondly, previous work required an oracle (usually the designer) to identify sets of events labeling the TS that were mapped to...

The unfolding method, initially introduced for systems modelled by Petri nets, is applied to synchronous products of transition systems, a model introduced by Arnold [2]. An unfolding procedure is provided which exploits the product structure of the model. Its performance is evaluated on a set of benchmarks. 1 Introduction The unfolding method is a partial order approach to the verification of concurrent systems introduced by McMillan in his Ph. D. Thesis [6]. A finite state system, modelled as a Petri net, is unfolded to yield an equivalent acyclic net with a simpler structure. This net is usually infinite, and so in general it cannot be used for automatic verification. However, it is possible to construct a complete finite prefix of it containing as much information as the infinite net itself: Loosely speaking, this prefix already contains all the reachable states of the system. The prefix is usually far smaller than the state space, and often smaller than a BDD representation of ...

The paper studies many-dimensional modal logics corresponding to products of Kripke frames. It proves results on axiomatisability, the finite model property and decidability for product logics, by applying a rather elaborated modal logic technique: p-morphisms, the finite depth method, normal forms, filtrations. Applications to first order predicate logics are considered too. The introduction and the conclusion contain a discussion of many related results and open problems in the area.

This paper gives a logical characterization of probabilistic bisimulation for Markov processes introduced in [BDEP97]. The thrust of that work was an extension of the notion of bisimulation to systems with continuous state spaces; for example for systems where the state space is the real numbers. In the present paper we study the logical characterization of probabilistic bisimulation for such general systems. This study revealed some unexpected results even for discrete probabilistic systems. ffl Bisimulation can be characterized by a very weak modal logic. The most striking feature is that one has no negation or any kind of negative proposition. ffl Bisimulation can be characterized by several inequivalent logics; we report five in this paper. ffl We do not need any finite branching assumption yet there is no need of infinitary conjunction. ffl The proofs that we give are of an entirely different character than the typical proofs of these results. They use quite subtle facts abou...

Abstract. Weighted automata are used to describe quantitative properties in various areas such as probabilistic systems, image compression, speech-to-text processing. The behaviour of such an automaton is a mapping, called a formal power series, assigning to each word a weight in some semiring. We generalize Büchi’s and Elgot’s fundamental theorems to this quantitative setting. We introduce a weighted version of MSO logic and prove that, for commutative semirings, the behaviours of weighted automata are precisely the formal power series definable with our weighted logic. We also consider weighted first-order logic and show that aperiodic series coincide with the first-order definable ones, if the semiring is locally finite, commutative and has some aperiodicity property. 1

In this report we present a large manufacturing example (7:01 10 states) that uses the Hierarchical Interface-based Supervisory Control method that we presented in [14]. We discuss the application of our method to the Atelier Inter-etablissement de Productique (AIP), a highly automated manufacturing system. We describe the system, and our supervisor design, closing by discussing the results of successfully applying our method to show that the system is nonblocking and that our supervisors are controllable. This example demonstrates that our method can be applied to interesting systems of realistic complexity that were previously far beyond our means.

The trace assertion method is a formal state machine based method for specifying module interfaces ([3, 15, 25, 28, 32, 36]). A module interface specification treats the module as a black-box, identifying all module's access programs (i.e. programs that can be invoked from outside of the module), and describing their externally visible effects. A formal model for the trace assertion method is proposed. The concept of step-traces is introduced and applied. The role of non-determinism, normal and exceptional behaviour, value functions and multi-object modules are discussed. The relationship with the Algebraic Specification ([9, 37]) is analyzed. Contents 1 Introduction 2 2 Introductory Examples 4 3 Alphabet 6 4 Normal and Exceptional Behaviour 7 5 Value Functions 8 6 Languages and Automata 9 6.1 Deterministic and Non-deterministic Automata : : : : : : : : : : : : : : : : : : : 9 6.2 Mealy Machines vs Automata : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 10 6.3 Right Congru...

State assignment problems still need satisfactory solutions to make asynchronous circuit synthesis more practical. A well-known example of such a problem is that of complete state coding (CSC), which happens when a pair of different states in a specification has the same binary encoding. A standard way to approach state coding conflicts is to insert new state signals into the original specification in such a way that the original behavior remains intact. This paper