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...

We show that there exists probabilistic finite automata with an isolated cutpoint and n states such that the smallest equivalent deterministic finite automaton contains Ω(2 n log log n log n ) states.

Li and Pedrycz [Y. M. Li, W. Pedrycz, Fuzzy finite automata and fuzzy regular expressions with membership values in lattice ordered monoids, Fuzzy Sets and Systems 156 (2005) 68–92] have proved fundamental results that provide different equivalentways to represent fuzzy languageswithmembership values in a lattice-orderedmonoid, and generalize the well-known results of the classical theory of fo...

We investigate the conversion of one-way nondeterministic finite automata and context-free grammars into Parikh equivalent oneway and two-way deterministic finite automata, from a descriptional complexity point of view. We prove that for each one-way nondeterministic automaton with n states there exist Parikh equivalent one-way and two-way deterministic automata with e √ n·lnn) and p(n) states,...

On every n-long input, every two-way finite automaton (fa) can reverse its head O(n) times before halting. A fawith few reversals is an automaton where this number is only o(n). For every h, we exhibit a language that requires Ω(2) states on every deterministic fa with few reversals, but only h states on a nondeterministic fa with few reversals.

The suffix automaton (resp. factor automaton) of a finite word w is the minimal deterministic automaton recognizing the set of suffixes (resp. factors) of w. We study the relationships between the structure of the suffix and factor automata and classical combinatorial parameters related to the special factors of w. We derive formulae for the number of states of these automata.We also characteri...

On every n-long input, every two-way finite automaton (fa) can reverse its head O(n) times before halting. A fawith few reversals is an automaton where this number is only o(n). For every h, we exhibit a language that requires Ω(2) states on every deterministic fa with few reversals, but only h states on a nondeterministic fa with few reversals.

In this paper we introduce the notion of merging states and merging systems and we use it for the classification of finite deterministic automata without initial and final states. We investigate the dependencies between the structure of an automaton described by merging systems and maximal lengths of minimal synchronizing words for automata which structures belong to the given class of merging ...

Traditional LTL model checking forms the product of a Büchi automaton — representing the negation of the specification — and a formal model of the (finite-state) system being verified. The resulting automaton is then checked for emptiness. An accepting run describes an execution of the model that violates the specification. Conversely, emptiness implies correctness. Many techniques have been de...

An algorithm is proposed that constructs a failure deterministic finite automaton in lockstep with the construction of a languageequivalent deterministic finite automaton. The states of both automata are assumed to be predefined and the failure deterministic finite automaton’s symbol and failure transitions are randomised. It is guaranteed that the latter remains free of divergent failure cycle...