In this paper, we define the notion of biRFSA which is a residual finate state automaton (RFSA) whose the reverse is also an RFSA. The languages recognized by such automata are called biRFSA languages. We prove that the canonical RFSA of a biRFSA language is a minimal NFA for this language and that each minimal NFA for this language is a sub-automaton of the canonical RFSA. This leads to a char...

Given a language L and a nondeterministic finite automaton M , we consider whether we can determine efficiently (in the size of M) if M accepts at least one word in L, or infinitely many words. Given that M accepts at least one word in L, we consider how long the shortest word can be. The languages L that we examine include the palindromes, the non-palindromes, the k-powers, the non-k-powers, t...

This work addresses the problem of the inference of non de-terministic automata (NFA) from given positive and negative samples. We propose here to consider this problem as a particular case of the inference of unambiguous nite state classiier. We are then able to present an eecient incompatibility NFA detection framework for state merging inference process.

We extend some of the classical connections between automata and logic due to Büchi (1960) [5] and McNaughton and Papert (1971) [12] to languages of finitely varying functions or ‘‘signals’’. In particular, we introduce a natural class of automata for generating finitely varying functions called ST-NFA’s, and show that it coincides in terms of language definability with a natural monadic second...

Alur, R. and D.L. Dill, A theory of timed automata, Theoretical Computer Science 126 (1994) 183-235. We propose timed (j&e) automata to model the behavior of real-time systems over time. Our definition provides a simple, and yet powerful, way to annotate state-transition graphs with timing constraints using finitely many real-valued clocks. A timed automaton accepts timed words-infinite sequenc...

We consider past pushdown timed automata that are discrete pushdown timed automata [15] with past-formulas as enabling conditions. Using past formulas allows a past pushdown timed automaton to access the past values of the finite state variables in the automaton. We prove that the reachability (i.e., the set of reachable configurations from an initial configuration) of a past pushdown timed aut...

Freivalds recently reported a construction of a 2-way probabilistic finite automaton A4 that recognizes the set Iambm : m b 1) with arbitrarily small probability of error. This result implies that probabilistic machines of this type are more powerful than their deterministic. nondeterministic, and alternating counterparts. Freivalds' construction has a negative feature: the automaton A4 runs in...

The simulation of deterministic pushdown automata defined over a one-letter alphabet by finite state automata is investigated from a descriptional complexity point of view. We show that each unary deterministic pushdown automaton of size s can be simulated by a deterministic finite automaton with a number of states that is exponential in s. We prove that this simulation is tight. Furthermore, i...

We examine questions involving nondeterministic finite automata where all states are final, initial, or both initial and final. First, we prove hardness results for the nonuniversality and inequivalence problems for these NFAs. Next, we characterize the languages accepted. Finally, we discuss some state complexity problems involving such automata.

In this thesis, we consider minimality and size reduction issues of one-tape and multitape automata. Although the topic of minimization of one-tape automata has been widely studied for many years, it seems that some issues have not gained attention. One of these issues concerns finding specific conditions on automata that imply their minimality in the class of nondeterministic finite automata (...