Minimal NFA Problems are Hard

Jiang, Tao; Ravikumar, Bala

doi:10.1137/0222067

Cited by 175 publications

(57 citation statements)

References 12 publications

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“…Both results are in strong contrast to what is known for bottom-up deterministic automata in the ranked case. Our np-hardness proof refines the proof techniques from [9,11], showing np-hardness of minimization for classes of finite automata with limited amount of non-determinism.…”

Section: Introductionmentioning

confidence: 96%

“…The question is particularly relevant for classes of deterministic automata, since minimization can be done both efficiently and leads to unique canonical representatives of regular languages, as is well-known for string languages and ranked tree languages. It is also well-known that minimal non-deterministic automata are neither unique, nor efficiently computable [9,11].…”

Section: Introductionmentioning

confidence: 99%

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Minimizing Tree Automata for Unranked Trees

Martens

Niehren

2005

Database Programming Languages

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Abstract. Automata for unranked trees form a foundation for XML schemas, querying and pattern languages. We study the problem of efficiently minimizing such automata. We start with the unranked tree automata (UTAs) that are standard in database theory, assuming bottomup determinism and that horizontal recursion is represented by deterministic finite automata. We show that minimal UTAs in that class are not unique and that minimization is np-hard. We then study more recent automata classes that do allow for polynomial time minimization. Among those, we show that bottom-up deterministic stepwise tree automata yield the most succinct representations.

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Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Minimizing Tree Automata for Unranked Trees

Martens

Niehren

2005

Database Programming Languages

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“…The proof of Theorem 2 is inspired by a proof by Jiang and Ravikumar (1993), showing that the normal set basis problem is NP-hard. See also (Björklund and Martens, 2012).…”

Section: Transition Minimisationmentioning

confidence: 99%

Compression of finite-state automata through failure transitions

Björklund

Zechner

2014

Theoretical Computer Science

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This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Compression of finite AbstractSeveral linear-time algorithms for automata-based pattern matching rely on failure transitions for efficient back-tracking. Like epsilon transitions, failure transition do not consume input symbols, but unlike them, they may only be taken when no other transition is applicable. At a semantic level, this conveniently models catch-all clauses and allows for compact language representation. This work investigates the transition-reduction problem for deterministic finite-state automata (DFA). The input is a DFA A and an integer k. The question is whether k or more transitions can be saved by replacing regular transitions with failure transitions. We show that while the problem is NP -complete, there are approximation techniques and heuristics that mitigate the computational complexity. We conclude by demonstrating the computational difficulty of two related minimisation problems, thereby cancelling the ongoing search for efficient algorithms.

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“…It is of practical relevance because regular languages are used in many applications, and one may like to represent the languages succinctly. While for nondeterministic automata the computation of an equivalent minimal automaton is PSPACE-complete [4] and thus highly intractable, the corresponding problem for deterministic automata is known to be effectively solvable in polynomial time [5]. An automaton is minimal if every other automaton with fewer states disagrees on acceptance for at least one input.…”

Section: Introductionmentioning

confidence: 99%

An nlogn Algorithm for Hyper-minimizing States in a (Minimized) Deterministic Automaton

Holzer

Maletti

2009

Implementation and Application of Automata

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Abstract. We improve a recent result [A. Badr: Hyper-Minimization in O(n 2 ). In Proc. CIAA, LNCS 5148, 2008] for hyper-minimized finite automata. Namely, we present an O(n log n) algorithm that computes for a given finite deterministic automaton (dfa) an almost equivalent dfa that is as small as possible-such an automaton is called hyper-minimal. Here two finite automata are almost equivalent if and only if the symmetric difference of their languages is finite. In other words, two almost-equivalent automata disagree on acceptance on finitely many inputs. In this way, we solve an open problem stated in [A. Badr, V. Geffert, I. Shipman: Hyper-minimizing minimized deterministic finite state automata. RAIRO Theor. Inf. Appl. 43(1), 2009] and by Badr. Moreover, we show that minimization linearly reduces to hyper-minimization, which is good evidence that our algorithm performs reasonably well.

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Minimal NFA Problems are Hard

Cited by 175 publications

References 12 publications

Minimizing Tree Automata for Unranked Trees

Minimizing Tree Automata for Unranked Trees

Compression of finite-state automata through failure transitions

An nlogn Algorithm for Hyper-minimizing States in a (Minimized) Deterministic Automaton

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