 
Summary: Universality of Rautomata with Value
Copying1
Parosh Aziz Abdulla, Pavel Krcal and Wang Yi2
Dept. of Information Technology,
Uppsala University, Sweden
Abstract
Rautomata 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 Rautomata, 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 Rautomata with value copying to universality of Rautomata, thus rendering the problem decidable.
The reduction replaces copy operations by nondeterministic 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
