2 research outputs found
History-deterministic Parikh Automata
Parikh automata extend finite automata by counters that can be tested for
membership in a semilinear set, but only at the end of a run. Thereby, they
preserve many of the desirable properties of finite automata. Deterministic
Parikh automata are strictly weaker than nondeterministic ones, but enjoy
better closure and algorithmic properties. This state of affairs motivates the
study of intermediate forms of nondeterminism. Here, we investigate
history-deterministic Parikh automata, i.e., automata whose nondeterminism can
be resolved on the fly. This restricted form of nondeterminism is well-suited
for applications which classically call for determinism, e.g., solving games
and composition. We show that history-deterministic Parikh automata are
strictly more expressive than deterministic ones, incomparable to unambiguous
ones, and enjoy almost all of the closure and some of the algorithmic
properties of deterministic automata.Comment: arXiv admin note: text overlap with arXiv:2207.0769
History-deterministic Parikh Automata
Parikh automata extend finite automata by counters that can be tested for membership in a semilinear set, but only at the end of a run. Thereby, they preserve many of the desirable properties of finite automata. Deterministic Parikh automata are strictly weaker than nondeterministic ones, but enjoy better closure and algorithmic properties. This state of affairs motivates the study of intermediate forms of nondeterminism. Here, we investigate history-deterministic Parikh automata, i.e., automata whose nondeterminism can be resolved on the fly. This restricted form of nondeterminism is well-suited for applications which classically call for determinism, e.g., solving games and composition. We show that history-deterministic Parikh automata are strictly more expressive than deterministic ones, incomparable to unambiguous ones, and enjoy almost all of the closure and some of the algorithmic properties of deterministic automata