An equilibrium in a repeated game with imperfect private moitoring is called a finite state equilibrium, if each player’s action on the equilibrium path is given by an automaton with a finite number of states. We provide a tractable general method to check the equilibrium conditions in this class. Our method is based on the belief-based approach and employs the theory of POMDP (Partially Observ...

Quantum finite automata with mixed states are proved to be super-exponentially more concise rather than quantum finite automata with pure states. It was proved earlier by A. Ambainis and R. Freivalds that quantum finite automata with pure states can have an exponentially smaller number of states than deterministic finite automata recognizing the same language. There was an unpublished ‘‘folk th...

A deterministic finite automaton (DFA) A is called a cover automaton (DFCA) for a finite language L over some alphabet Σ if L = L(A) ∩ Σ≤l, with l being the length of some longest word in L. Thus a word w ∈ Σ∗ is in L if and only if |w| ≤ l and w ∈ L(A). The DFCA A is minimal if no DFCA for L has fewer states. In this paper, we present an algorithm which converts an n–state DFA for some finite ...

A deterministic finite automaton (DFA) A is called a cover automaton (DFCA) for a finite language L over some alphabet Σ if L = L(A) ∩ Σ≤l, with l being the length of some longest word in L. Thus a word w ∈ Σ∗ is in L if and only if |w| ≤ l and w ∈ L(A). The DFCA A is minimal if no DFCA for L has fewer states. In this paper, we present an algorithm which converts an n–state DFA for some finite ...

A cover automaton of a finite language L is a finite automaton that accepts all words in L and possibly other words that are longer than any word in L. An algorithm for constructing a minimal cover automaton of a finite language L is given in a recent paper. This paper goes a step further by proposing a procedure for constructing all minimal cover automata of a given finite language L. The conc...

Unary self-verifying symmetric difference automata have a known tight bound of [Formula: see text] for their state complexity. We now consider the non-unary case and show that, every text], there is regular language accepted by nondeterministic automaton with states, such that its equivalent minimal deterministic finite has states. Furthermore, given any SV-XNFA it possible, up to isomorphism, ...

Determining the minimum number of states required by a finite automaton to separate a given pair of different words is an important problem. In this paper, we consider this problem for quantum automata (QFAs). We show that 2-state QFAs can separate any pair of words in nondeterministic acceptance mode and conjecture that they can separate any pair also with zero-error. Then, we focus on (a more...

In this paper, we show that for any BL-general L-fuzzy automaton (BL-GLFA) there exists a complete deterministic accessible reduced BL-general L-fuzzy automaton that recognizing the behavior of the BL-GLFA. Also, we prove that for any finite realization β, there exists a minimal complete deterministic BL-GLFA recognizing β. We prove any complete deterministic accessible reduced BL-GLFA is a min...