Size (the number of states) of finite probabilistic automata with an isolated cut-point can be exponentially smaller than the size of any equivalent finite deterministic automaton. The result is presented in two versions. The first version depends on Artin’s Conjecture (1927) in Number Theory. The second version does not depend on conjectures but the numerical estimates are worse. In both versi...

The concept of Deterministic Finite Cover Automata (DFCA) was introduced at WIA ’98, as a more compact representation than Deterministic Finite Automata (DFA) for finite languages. In some cases representing a finite language using a Non-deterministic Finite Automata (NFA) may significantly reduce the number of required states. The combined power of the succinctness of the representation of fin...

in this paper, we use game theory to describe the emergence of self-organization and consequent pattern formation through communicative cooperation in bacillus subtilis colonies. the emergence of cooperative regime is modelled as an n-player assurance game, with the bacterial colonies as individual players. the game is played iteratively through cooperative communication, and mediated by exchan...

Inspired by failure functions found in classical pattern matching algorithms, a failure deterministic finite automaton (FDFA) is defined as a formalism to recognise a regular language. An algorithm, based on formal concept analysis, is proposed for deriving from a given deterministic finite automaton (DFA) a language-equivalent FDFA. The FDFA’s transition diagram has fewer arcs than that of the...

A well-known decision procedure for Presburger arithmetic uses deterministic finite-state automata. While the complexity of the decision procedure for Presburger arithmetic based on quantifier elimination is known (roughly, there is a double-exponential non-deterministic time lower bound and a triple exponential deterministic time upper bound), the exact complexity of the automata-based procedu...

Inoue et al. introduced an automaton on a twodimensional tape, which decides acceptance or rejection of an input tape by scanning the tape from various sides by various automata which move one way, and investigated the accepting power of such an automaton. This paper continues the investigation of this type of automata, especially, ∨-type automata (obtained by combining four three-way two-dimen...

We study structural restrictions on biautomata such as, e.g., acyclicity, permutation-freeness, strongly permutation-freeness, and orderability, to mention a few. We compare the obtained language families with those induced by deterministic finite automata with the same property. In some cases, it is shown that there is no difference in characterization between deterministic finite automata and...