Combinatory automaton

We prove that semigroups generated by reversible two-state Mealy automata have remarkable growth properties: they are either finite or free. We give an effective procedure to decide finiteness or freeness of such semigroups when the generating automaton ...

The concept of an automaton group generalizes easily to semigroups, and the systematic study of this area is beginning. This paper aims to contribute to that study. The basic theory of automaton semigroups is briefly reviewed. Various natural semigroups ...

Quantitative languages are an extension of boolean languages that assign to each word a real number. Mean-payoff automata are finite automata with numerical weights on transitions that assign to each infinite path the long-run average of the transition ...