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 properties of deterministic automata. This restricted form of nondeterminism is well-suited for applications which classically call for determinism, e.g., solving games and composition. Here, we investigate history-deterministic Parikh automata, i.e., automata whose nondeterminism can be resolved on the fly. In a deterministic automaton, there are a set of states, a set of inputs, and a function that brings the result to the next state. This state of affairs motivates the study of intermediate forms of nondeterminism. A deterministic automaton is a computer science concept where transition results are determined by the input, and no random arbitration occurs. Deterministic Parikh automata are strictly weaker than nondeterministic ones, but enjoy better closure and algorithmic properties. Note that the above definitions do not ascribe any meaning to the strings of the language.
Thereby, they preserve many of the desirable properties of finite automata. Lecture 1: Deterministic Finite State Automata (DFA) Lorenzo De Stefani Fall 2020 Outline What is a Finite State Automaton DFA definition Example DFA construction The language of a DFA Regular Operations Closure under union Closure under concatenation From Sipser Chapter 1. Download a PDF of the paper titled History-deterministic Parikh Automata, by Enzo Erlich and 4 other authors Download PDF Abstract: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.
