Improved limitedness theorems on finite automata with distance functions
Theoretical Computer Science - Special issue on theoretical computer science, algebra and combinatorics
Factorization forests of finite height
Theoretical Computer Science - Special issue on theoretical computer science, algebra and combinatorics
Limitedness theorem on finite automata with distance functions: an algebraic proof
Theoretical Computer Science
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We introduce R-automata--- finite state machines which operate on a finite number of unbounded counters. The values of the counters can be incremented, reset to zero, or left unchanged along the transitions. R-automata can be, for example, used to model systems with resources (modeled by the counters) which are consumed in small parts but which can be replenished at once. We define the language accepted by an R-automaton relative to a natural number Das the set of words allowing a run along which no counter value exceeds D. As the main result, we show decidability of the universality problem, i.e., the problem whether there is a number Dsuch that the corresponding language is universal. We present a proof based on finite monoids and the factorization forest theorem. This theorem was applied for distance automata in [12]--- a special case of R-automata with one counter which is never reset. As a second technical contribution, we extend the decidability result to R-automata with Büchi acceptance conditions.