We consider deterministic and nondeterministic finite automata with acceptance conditions that rely on the whole history of a computation on a given word and not only on the last state of the computation under consideration. Formally, these conditions can be seen as the natural analogies of the Büchi and Muller acceptance for finite automata on infinite words. We study the computational power o...

This paper describes a non-conventional method for compiling (phonological or morpho-syntactic) context restriction (CR) constraints into non-deterministic automata in finite-state tools and surface parsing systems. The method reduces any CR into a simple one that constraints the occurrences of the empty string and represents right contexts with co-determististic states. In cases where a fully ...

The result proved in this paper is that for the elements of some infinite class of deterministic context-free languages the size of deterministic pushdown amomata needed to describe them is not recursively bounded by the size of the smallest unambiguous context-free grammars that generate them. This is a quantitative explanation of the fact that some languages require large descriptions in term...

Symbolic automata allow transitions to carry predicates over rich alphabet theories, such as linear arithmetic, and therefore extend classic automata to operate over infinite alphabets, such as the set of rational numbers. Existing automata algorithms rely on the alphabet being finite, and generalizing them to the symbolic setting is not a trivial task. In our earlier work, we proposed new tech...

Recently, a characterization of the class of nondeterministic finite automata (NFAs) for which determinization results in a minimal deterministic finite automaton (DFA), was given in [2]. We present a similar result for the case of symmetric difference NFAs. Also, we show that determinization of any minimal symmetric difference NFA produces a minimal DFA.

We introduce a new class of probabilistic automata: Probabilistic Residual Finite State Automata. We show that this class can be characterized by a simple intrinsic property of the stochastic languages they generate (the set of residual languages is finitely generated) and that it admits canonical minimal forms. We prove that there are more languages generated by PRFA than by Probabilistic Dete...

Motivated by formal models recently proposed in the context of XML, we study automata and logics on strings over infinite alphabets. These are conservative extensions of classical automata and logics defining the regular languages on finite alphabets. Specifically, we consider register and pebble automata, and extensions of first-order logic and monadic second-order logic. For each type of auto...

We resolve an open problem raised by Ravikumar and Ibarra [SIAM J. Comput., 18 (1989), pp. 1263–1282] on the succinctness of representations relating to the types of ambiguity of finite automata. We show that there exists a family of nondeterministic finite automata {An} over a two-letter alphabet such that, for any positive integer n, An is exponentially ambiguous and has n states, whereas the...

We introduce a notion of partial derivative of a regular expression and apply it to finite automaton constructions. The notion is a generalization of the known notion of word derivative due to Brzozowski: partial derivatives are related to non-deterministic finite automata (NFA’s) in the same natural way as derivatives are related to deterministic ones (DFA’s). We give a constructive definition...

Merging states in finite automata is a main method of reducing the size of the representation of regular languages. The process has been extensively studied for deterministic finite automata (DFA), where the conditions for merging states can be efficiently computed. The matter is more complex in the case of nondeterministic finite automata (NFA), where merging states can be done in different wa...