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Universality of R-automata with Value Parosh Aziz Abdulla, Pavel Krcal and Wang Yi2

Summary: Universality of R-automata with Value
Parosh Aziz Abdulla, Pavel Krcal and Wang Yi2
Dept. of Information Technology,
Uppsala University, Sweden
R-automata are finite state machines extended with counters which can be incremented or reset to zero
along the transitions. The universality question asks whether there is a constant D such that all words are
accepted by some run along which no counter exceeds D. It has been shown in [2] that this question is
decidable. In this paper, we add one more operation to R-automata, namely the operation which can copy
the value of a counter into another one. The result of this paper is a reduction of the universality problem
for R-automata with value copying to universality of R-automata, thus rendering the problem decidable.
The reduction replaces copy operations by non-deterministic resets together with a mechanism ensuring
that the number of such replacements is bounded between each two resets of a value.
Keywords: Distance automata with resets and copying, universality, decidability.
1 Introduction
Finite state machines usually serve as word acceptors, where the accepting condition
is expressed in terms of the last reached state. For the acceptance of a word, it does
not matter what has happened along the run, as long as we end up in an accepting
state. One can also introduce a notion of the cost into finite automata by setting


Source: Abdulla, Parosh Aziz - Department of Information Technology, Uppsala Universitet


Collections: Computer Technologies and Information Sciences