On the degree of ambuguity of finite automata
Proceedings of the 12th symposium on Mathematical foundations of computer science 1986
Relating the type of ambiguity of finite automata to the succinctness of their representation
SIAM Journal on Computing
Communication complexity and parallel computing
Communication complexity and parallel computing
Separating Exponentially Ambiguous Finite Automata from Polynomially Ambiguous Finite Automata
SIAM Journal on Computing
Introduction to Automata Theory, Languages and Computability
Introduction to Automata Theory, Languages and Computability
Measures of Nondeterminism in Finite Automata
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Minimizing NFA's and regular expressions
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
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The degree of nondeterminism of a finite automaton can be measured by means of its ambiguity function. In many instances, whenever automata are allowed to be (substantially) less ambiguous, it is known that the number of states needed to recognize at least some languages increases exponentially. However, when comparing constantly ambiguous automata with polynomially ambiguous ones, the question whether there are languages such that the inferior class of automata requires exponentially many states more than the superior class to recognize them is still an open problem. The purpose of this paper is to suggest a family of languages that seems apt for a proof of this (conjectured) gap. As a byproduct, we derive a new variant of the proof of the existence of a superpolynomial gap between polynomial and fixed-constant ambiguity. Although our candidate languages are defined over a huge alphabet, we show how to overcome this drawback.