In this paper, we describe a new method for constructing minimal, deterministic, acyclic finitestate automata from a set of strings. Traditional methods consist of two phases: the first to construct a trie, the second one to minimize it. Our approach is to construct a minimal automaton in a single phase by adding new strings one by one and minimizing the resulting automaton on-the-fly. We prese...

In this paper we investigate from a statistical point of view the expected compression ratio between the size of a minimal Deterministic Finite Cover Automaton (DFCA) and the size of the minimal corresponding Determinitic Finite Automaton (DFA). Using sound statistical methods, we extend the experimental study done in [16], thus obtaining a much better picture of the compression power of DFCAs....

We study minimal odd rankings (as defined by Kupferman and Vardi[KV01]) for run-DAGs of words in the complement of a nondeterministic Büchi automaton. We present an optimized version of the ranking based complementation construction of Friedgut, Kupferman and Vardi [FKV06] and Schewe’s[Sch09] variant of it, such that every accepting run of the complement automaton assigns a minimal odd ranking ...

The article continues the study of the genus of regular languages that the author introduced in a 2012 paper. We show that the minimal finite deterministic automaton of a regular language can be arbitrary far away from a finite deterministic automaton realizing the minimal genus and computing the same language both in terms of the difference of genera and in terms of the difference in size. How...

A condition characterizing the class of regular languages which have several nonisomorphic minimal reversible automata is presented. The condition concerns the structure of the minimum automaton accepting the language under consideration. It is also observed that there exist reduced reversible automata which are not minimal, in the sense that all the automata obtained by merging some of their e...

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.

This paper is a survey on the universal automaton, which is an automaton canonically associated with every language. In the last forty years, many objects have been defined or studied, that are indeed closely related to the universal automaton. We first show that every automaton that accepts a given language has a morphic image which is a subautomaton of the universal automaton of this language...

A word w is called synchronizing (recurrent, reset) word of an automaton if w sends all states of the automaton on a unique state. Cerny had conjectured in 1964 that an n-state automaton with non-empty set of synchronizing words possesses a synchronizing word of length not greater than (n 1)2. We consider automata accepting star-free languages (or aperiodic, viz all subgroups of the syntactic m...

We consider decision problems where the agent has bounded memory and makes decisions using a finite state automaton. For any automaton, we show there exist equivalent automata with minimal randomization. We introduce a new criterion for interim rationality called weak admissibility and demonstrate that if memory states are not wasted, the nature of transitions are uniquely defined by the criter...