Abstract. The minimum consistent DFA problem is that of finding a DFA with as few states as possible that is consistent with a given sample (a finite collection of words, each labeled as to whether the DFA found should accept or reject). Assuming that P # NP, it is shown that for any constant k, no polynomial-time algorithm can be guaranteed to find a consistent DFA with fewer than opt ~ states, where opt is the number of states in the minimum state DFA consistent with the sample. This result holds even if the alphabet is of constant size two, and if the algorithm is allowed to produce an NFA, a regular expression, or a regular grammar that is consistent with the sample. A similar nonapproximability result is presented for the problem of finding small consistent linear grammars. For the case of finding minimum consistent DFAs when the alphabet is not of constant size but instead is allowed to vay with the problem specification, the slightly

Testing is a trade-off between increased confidence in the correctness of the implementation under test and constraints on the amount of time and effort that can be spent in testing. Therefore, the coverage, or adequacy of the test suite, becomes a very important issue. In this paper, we analyze basic ideas underlying the techniques for fault coverage analysis and assurance mainly developed in the context of protocol conformance testing based on finite state models. Special attention is paid to parameters which determine the testability of a given specification and influence the length of a test suite which guarantees complete fault coverage. We also point out certain issues which need further study. 1. INTRODUCTION Testing is a critical phase in the development life cycle for any hardware and software system, and in particular for communication systems for which it ensures the conformance to the relevant standards and compatibility or interoperability with other systems. Testing con...

A cover-automaton A of a finite language L ` \Sigma is a finite deterministic automaton (DFA) that accepts all words in L and possibly other words that are longer than any word in L. A minimal deterministic finite cover automaton (DFCA) of a finite language L usually has a smaller size than a minimal DFA that accept L. Thus, cover automata can be used to reduce the size of the representations of finite languages in practice. In this paper, we describe an efficient algorithm that, for a given DFA accepting a finite language, constructs a minimal deterministic finite coverautomaton of the language. We also give algorithms for the boolean operations on deterministic cover automata, i.e., on the finite languages they represent. Key words: Finite languages,Deterministic Finite Automata,Cover Language,Deterministic Cover Automata 1 Introduction Regular languages and finite automata are widely used in many areas such as lexical analysis, string matching, circuit testing, image compression,...

The principal objective of this paper is to lift basic concepts of the classical automata theory from discrete to continuous (real) time. It is argued that the set of nite memory retrospective functions is the set of functions realized by nite state devices. We show that the nite memory retrospective functions are speed-independent, i.e., they are invariant under `stretchings' of the time axis. Therefore, such functions cannot deal with metrical aspects of the reals.

We consider an interpretation of monadic second-order logic of order in the continuous time structure of finitely variable signals and show the decidability of monadic logic in this structure. The expressive power of monadic logic is illustrated by providing a straightforward meaning preserving translation into monadic logic of three typical continuous time specification formalism: Temporal Logic of Reals [2], Restricted Duration Calculus [4], and the Propositional fragment of Mean Value Calculus [6]. As a by-product of the decidability of monadic logic we obtain that the above formalisms are decidable even when extended by quantifiers. 1 Introduction In the recent years systems whose behavior change in the continuous (real) time were extensively investigated. Hybrid and control systems are prominent examples of real time systems. A number of formalisms for specification of real time behavior were suggested in the literature. Some of these formalisms (e.g., timed automata [1]) exten...

We propose a new algorithm for the inference of the minimum size deterministic automaton consistent with a prespecified set of input/output strings. Our approach improves a well known search algorithm proposed by Bierman, by incorporating a set of techniques known as dependency directed backtracking. These techniques have already been used in other applications, but we are the first to apply them to this problem. The results show that the application of these techniques yields an algorithm that is, for the problems studied, orders of magnitude faster than existing approaches.

Abstract—Learning a Deterministic Finite Automaton (DFA) from a training set of labeled strings is a hard task that has been much studied within the machine learning community. It is equivalent to learning a regular language by example and has applications in language modeling. In this paper, we describe a novel evolutionary method for learning DFA that evolves only the transition matrix and uses a simple deterministic procedure to optimally assign state labels. We compare its performance with the Evidence Driven State Merging (EDSM) algorithm, one of the most powerful known DFA learning algorithms. We present results on random DFA induction problems of varying target size and training set density. We also study the effects of noisy training data on the evolutionary approach and on EDSM. On noisefree data, we find that our evolutionary method outperforms EDSM on small sparse data sets. In the case of noisy training data, we find that our evolutionary method consistently outperforms EDSM, as well as other significant methods submitted to two recent competitions. Index Terms—Grammatical inference, finite state automata, random hill climber, evolutionary algorithm. 1

this paper we consider the fragment of Lamport's Temporal Logic of Action where variables can only receive boolean values (BTLA). First we investigate the question of existence of a meaning preserving translation from BTLA into L

. The paper compares the expressive power of monadic second order logic of order, a fundamental formalism in mathematical logic and theory of computation, with that of a fragment of Temporal Logic of Actions introduced by Lamport for specifying the behavior of concurrent systems. 1 Introduction The Temporal Logic of Actions (TLA) was introduced by Lamport [3] as a logic for specifying concurrent systems and reasoning about them. One of the main differences of TLA from other discrete time temporal logics is its inability to specify that one state should immediately be followed by the other state, though it can be specified that one state is followed by the other state at some later time. Lamport [2] argued in favor of this decision `The number of steps in a Pascal implementation is not a meaningful concept when one gives an abstract, high level specification'. For example, programs like P r 1 :: x := T rue; y := F alse and P r 2 :: x := T rue; Skip; y := F alse are not distinguishable...

We consider an interpretation of monadic second-order logic of order in the continuous time structure of finitely variable signals. We provide a characterization of the expressive power of monadic logic. As a by-product of our characterization we show that many fundamental theorems which hold in the discrete time interpretation of monadic logic are still valid in the continuous time interpretation.