Unique decodability of bigram counts by finite automata

TL;DR

This paper investigates whether bigram count data can be uniquely decoded using finite automata, providing an efficient construction for nondeterministic automata and demonstrating exponential complexity for deterministic automata.

Contribution

It introduces a polynomial-size nondeterministic automaton for deciding unique decodability and proves exponential lower bounds for deterministic automata.

Findings

Polynomial-size nondeterministic automaton constructed

Deterministic automaton requires exponentially many states

Decidability of unique decodability via finite automata

Abstract

We revisit the problem of deciding whether a given string is uniquely decodable from its bigram counts by means of a finite automaton. An efficient algorithm for constructing a polynomial-size nondeterministic finite automaton that decides unique decodability is given. Conversely, we show that the minimum deterministic finite automaton for deciding unique decodability has at least exponentially many states in alphabet size.