Information and Computation
Mixed product and asynchronous automata
Theoretical Computer Science
Decidability of the Star Problem in A*×b *
Information Processing Letters
Synthesis of nondeterministic asynchronous automata
Semantics of programming languages and model theory
New results on the star problem in trace monoids
Information and Computation
Partial commutation and traces
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Automata, Languages, and Machines
Automata, Languages, and Machines
The Book of Traces
Some Decision Problems for Traces
LFCS '97 Proceedings of the 4th International Symposium on Logical Foundations of Computer Science
Some Trace Monoids Where Both the Star Problem and the Finite Power Property Problem are Decidable
MFCS '94 Proceedings of the 19th International Symposium on Mathematical Foundations of Computer Science 1994
The "Last" Decision Problem for Rational Trace Languages
LATIN '92 Proceedings of the 1st Latin American Symposium on Theoretical Informatics
STACS '94 Proceedings of the 11th Annual Symposium on Theoretical Aspects of Computer Science
Two techniques in the area of the star problem in trace monoids
Theoretical Computer Science
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We deal with the star problem in trace monoids which means to decide whether the iteration of a recognizable trace language is recognizable. We consider trace monoids Kn = {a1, b1}* × ... × {an, bn}*. Our main result asserts that the star problem is decidable in some trace monoid M iff it is decidable in the biggest Kn submonoid in M. Consequently, future research on the star problem can focus on the trace monoids Kn. We develop the main results of the paper for the finite power problem. Then, we establish the link to the star problem by applying the recently shown decidability equivalence between the star problem and the finite power problem (D. Kirsten and G. Richomme, 2001, Theory Comput. Systems 34, 193-227).