Deciding unique decodability of bigram counts via finite automata
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 effi...
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| Veröffentlicht in: | Journal of computer and system sciences Jg. 80; H. 2; S. 450 - 456 |
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| Sprache: | Englisch |
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01.03.2014
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| 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.
•We prove that the bigram-decodable strings form a regular language.•We construct a cubic-sized NFA for recognizing this language.•We show how to simulate this NFA efficiently.•We give a lower bound on the size of any DFA for this language. |
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| AbstractList | 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. 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. •We prove that the bigram-decodable strings form a regular language.•We construct a cubic-sized NFA for recognizing this language.•We show how to simulate this NFA efficiently.•We give a lower bound on the size of any DFA for this language. |
| Author | Kontorovich, Aryeh Trachtenberg, Ari |
| Author_xml | – sequence: 1 givenname: Aryeh surname: Kontorovich fullname: Kontorovich, Aryeh email: karyeh@cs.bgu.ac.il organization: Department of Computer Science, Ben-Gurion University, Beer Sheva 84105, Israel – sequence: 2 givenname: Ari surname: Trachtenberg fullname: Trachtenberg, Ari email: trachten@bu.edu organization: Department of Electrical & Computer Engineering, Boston University, 8 Saint Maryʼs Street, Boston, MA 02215, United States |
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| Cites_doi | 10.1093/bioinformatics/bth205 10.1016/j.jcss.2007.10.004 10.1137/060651380 10.1109/TPDS.2006.148 10.1016/j.tcs.2004.10.010 |
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| Keywords | Sequence reconstruction Eulerian graph Finite-state automata Uniqueness |
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| Title | Deciding unique decodability of bigram counts via finite automata |
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