We investigate extensions of temporal logic by connectives defined by finite automata on infinite words. We consider three different logics, corresponding to three different types of acceptance conditions (finite, looping and repeating) for the automata. It turns out, however, that these logics all have the same expressive power and that their decision problems are all PSPACE-complete. We also investigate connectives defined by alternating automata and show that they do not increase the expressive power of the logic or the complexity of the decision problem. 1 Introduction For many years, logics of programs have been tools for reasoning about the input/output behavior of programs. When dealing with concurrent or nonterminating processes (like operating systems) there is, however, a need to reason about infinite computations. Thus, instead of considering the first and last states of finite computations, we need to consider the infinite sequences of states that the program goes through...

Abstract. This paper presents algorithms for the automatic synthesis of real-time controllers by nding a winning strategy for certain games de ned by the timed-automata of Alur and Dill. In such games, the outcome depends on the players ' actions as well as on their timing. We believe that these results will pave theway for the application of program synthesis techniques to the construction of real-time embedded systems from their speci cations. 1

In this work we tackle the following problem: given a timed automaton, restrict its transition relation in a systematic way so that all the remaining behaviors satisfy certain properties. This is an extension of the problem of controller synthesis for discrete event dynamical systems, where in addition to choosing among actions, the controller have the option of doing nothing and let the time pass. The problem is formulated using the notion of a real-time game, and a winning strategy is constructed as a fixed-point of an operator on the space of states and clock configurations.

. This paper first describes the structure and results of the Abbadingo One DFA Learning Competition. The competition was designed to encourage work on algorithms that scale well---both to larger DFAs and to sparser training data. We then describe and discuss the winning algorithm of Rodney Price, which orders state merges according to the amount of evidence in their favor. A second winning algorithm, of Hugues Juille, will be described in a separate paper. Part I: Abbadingo 1 Introduction The Abbadingo One DFA Learning Competition was organized by two of the authors (Lang and Pearlmutter) and consisted of a set of challenge problems posted to the internet and token cash prizes of $1024. The organizers had the following goals: -- Promote the development of new and better algorithms. -- Encourage learning theorists to implement some of their ideas and gather empirical data concerning their performance on concrete problems which lie beyond proven bounds, particulary in the direction o...

Approximate inference of finite state machines from sparse labeled examples has been proved NP-hard when an adversary chooses the target machine and the training set [Ang78, KV89, PW89]. We have, however, empirically found that DFA's are approximately learnable from sparse data when the target machine and training set are selected at random. 1 A Greedy Learning Algorithm Trakhtenbrot and Barzdin described the following polynomial time algorithm for constructing the smallest DFA consistent with a complete labeled training set [TB73]. The input to the algorithm is the prefix-tree acceptor which directly embodies the training set. This tree is collapsed into a smaller graph by merging all pairs of states that represent compatible mappings from string suffixes to labels. The algorithm contains two nested loops. In the outer loop, each node i is visited in breadth-first order starting at the tree's root. In the inner loop, each node j between the root and node i \Gamma 1 is evaluated for ...

This paper describes new and efficient algorithms for learning deterministic finite automata. Our approach is primarily distinguished by two features: (1) the adoption of an average-case setting to model the ``typical'' labeling of a finite automaton, while retaining a worst-case model for the underlying graph of the automaton, along with (2) a learning model in which the learner is not provided with the means to experiment with the machine, but rather must learn solely by observing the automaton's output behavior on a random input sequence. The main contribution of this paper is in presenting the first efficient algorithms for learning nontrivial classes of automata in an entirely passive learning model. We adopt an on-line learning model in which the learner is asked to predict the output of the next state, given the next symbol of the random input sequence; the goal of the learner is to make as few prediction mistakes as possible. Assuming the learner has a means of resetting the target machine to a fixed start state, we first present an efficient algorithm that

This paper revisits the theory of regular inference, in particular by extending the definition of structural completeness of a positive sample and by demonstrating two basic theorems. This framework enables to state the regular inference problem as a search through a boolean lattice built from the positive sample. Several properties of the search space are studied and generalization criteria are discussed. In this framework, the concept of border set is introduced, that is the set of the most general solutions excluding a negative sample. Finally, the complexity of regular language identification from both a theoritical and a practical point of view is discussed. 1 Introduction Regular inference is the process of learning a regular language from a set of examples, consisting of a positive sample, i.e. a finite subset of a regular language. A negative sample, i.e. a finite set of strings not belonging to this language, may also be available. This problem has been studied as early as th...

We recall briefly in this paper the formal theory of regular grammatical inference from positive and negative samples of the language to be learned. We state this problem as a search toward an optimal element in a boolean lattice built from the positive information. We explain how a genetic search technique may be applied to this problem and we introduce a new set of genetic operators. In view of limiting the increasing complexity as the sample size grows, we propose a semi-incremental procedure. Finally, an experimental protocol to assess the performance of a regular inference technique is detailed and comparative results are given. 1 Introduction Grammatical Inference is an instance of the Inductive Learning problem which can be formulated as the task of discovering common structures in examples which are supposed to be generated by the same process. In this particular case, the examples are sentences defined on a specific alphabet and the common structures are represented by a gram...

We investigate in this thesis problems concerning the complexity of translation among, and decision procedure for, different types of finite automata on infinite words (!- automata). An !-automaton is the same as usual finite automata over finite strings but it accepts or rejects infinite strings. It may be either deterministic or nondeterministic, and may have different types of acceptance condition. Our main result is a new, simpler, determinization construction that yields a single exponent upper bound for the translation of any Buchi nondeterministic !-automaton into a deterministic !-auomaton. This construction is optimal. We also look at the complexity of the complementation problem for different types of !-automata, and, among other results, obtain an exponential complementation for Streett !-automata. These results can be used to improve the complexity of decision procedures for different logics that use automata-theoretic techniques. Acknowledgement First and foremost, I o...

Even if access to the internal structure of the tested system is possible, it is not always a good idea to use it when performing tests, as this may lead to a bias in the testing process. Furthermore, the