Deciding unique decodability of bigram counts via finite automata

Aryeh Kontorovich; Ari Trachtenberg

doi:10.1016/j.jcss.2013.09.003

Deciding unique decodability of bigram counts via finite automata

Aryeh Kontorovich, Ari Trachtenberg

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We revisit the problem of deciding by means of a finite automaton whether a string is uniquely decodable from its bigram counts. An efficient algorithm for constructing a polynomial-size Nondeterministic Finite Automaton (NFA) that decides unique decodability is given. This NFA may be simulated efficiently in time and space. Conversely, we show that the minimum deterministic finite automaton for deciding unique decodability has exponentially many states in alphabet size, and compute the correct order of magnitude of the exponent.

Original language	English
Pages (from-to)	450-456
Number of pages	7
Journal	Journal of Computer and System Sciences
Volume	80
Issue number	2
DOIs	https://doi.org/10.1016/j.jcss.2013.09.003
State	Published - 1 Jan 2014

Keywords

Eulerian graph
Finite-state automata
Sequence reconstruction
Uniqueness

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science
Computer Networks and Communications
Computational Theory and Mathematics
Applied Mathematics

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10.1016/j.jcss.2013.09.003

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title = "Deciding unique decodability of bigram counts via finite automata",

abstract = "We revisit the problem of deciding by means of a finite automaton whether a string is uniquely decodable from its bigram counts. An efficient algorithm for constructing a polynomial-size Nondeterministic Finite Automaton (NFA) that decides unique decodability is given. This NFA may be simulated efficiently in time and space. Conversely, we show that the minimum deterministic finite automaton for deciding unique decodability has exponentially many states in alphabet size, and compute the correct order of magnitude of the exponent.",

keywords = "Eulerian graph, Finite-state automata, Sequence reconstruction, Uniqueness",

author = "Aryeh Kontorovich and Ari Trachtenberg",

note = "Funding Information: We thank the referees for carefully reading the manuscript and making useful suggestions. Arnold Filtzer and Omrit Naftali assisted in proving Lemma 5 . The first author was supported in part by the Israel Science Foundation (grant No. 1141/12 ).",

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N2 - We revisit the problem of deciding by means of a finite automaton whether a string is uniquely decodable from its bigram counts. An efficient algorithm for constructing a polynomial-size Nondeterministic Finite Automaton (NFA) that decides unique decodability is given. This NFA may be simulated efficiently in time and space. Conversely, we show that the minimum deterministic finite automaton for deciding unique decodability has exponentially many states in alphabet size, and compute the correct order of magnitude of the exponent.

AB - We revisit the problem of deciding by means of a finite automaton whether a string is uniquely decodable from its bigram counts. An efficient algorithm for constructing a polynomial-size Nondeterministic Finite Automaton (NFA) that decides unique decodability is given. This NFA may be simulated efficiently in time and space. Conversely, we show that the minimum deterministic finite automaton for deciding unique decodability has exponentially many states in alphabet size, and compute the correct order of magnitude of the exponent.

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KW - Finite-state automata

KW - Sequence reconstruction

KW - Uniqueness

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JO - Journal of Computer and System Sciences

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Deciding unique decodability of bigram counts via finite automata

Abstract

Keywords

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