The Abstract Theory of Automata

Glushkov, V. M.

doi:10.1070/rm1961v016n05abeh004112

Cited by 394 publications

(197 citation statements)

References 17 publications

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“…An easy, linear time, algorithm for calculating the First-set has been given by many others, e.g., Glushkov [6] and Yamada & McNaughton [9].…”

Section: Definition 1 (Regular Expressions)mentioning

confidence: 99%

The Inclusion Problem for Regular Expressions

Hovland

2010

Language and Automata Theory and Applications

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Abstract. This paper presents a new polynomial-time algorithm for the inclusion problem for certain pairs of regular expressions. The algorithm is not based on construction of finite automata, and can therefore be faster than the lower bound implied by the Myhill-Nerode theorem. The algorithm automatically discards unnecessary parts of the right-hand expression. In these cases the right-hand expression might even be 1-ambiguous. For example, if r is a regular expression such that any DFA recognizing r is very large, the algorithm can still, in time independent of r, decide that the language of ab is included in that of (a + r)b. The algorithm is based on a syntax-directed inference system. It takes arbitrary regular expressions as input, and if the 1-ambiguity of the right-hand expression becomes a problem, the algorithm will report this.

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“…An easy, linear time, algorithm for calculating the First-set has been given by many others, e.g., Glushkov [6] and Yamada & McNaughton [9].…”

Section: Definition 1 (Regular Expressions)mentioning

confidence: 99%

The Inclusion Problem for Regular Expressions

Hovland

2010

Language and Automata Theory and Applications

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“…All classical conversions [1,3,9,12] produce ε-free NFAs with worst-case size quadratic in the length of the given regular expression and for some time this was assumed to be optimal [10]. But then Hromkovic, Seibert and Wilke [7] constructed ε-free NFAs with surprisingly only O(n(log 2 n) 2 ) transitions for regular expressions of length n and this transformation can even be implemented to run in time O(n · log 2 n + m), where m is the size of the output [4].…”

Section: Introductionmentioning

confidence: 99%

Regular Expressions and NFAs Without ε-Transitions

Schnitger

2006

Stacs 2006

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Abstract. We consider the problem of converting regular expressions into ε-free NFAs with as few transitions as possible. If the regular expression has length n and is defined over an alphabet of size k, then the previously best construction uses O(n·min{k, log 2 n}·log 2 n) transitions. We show that O(n · log 2 2k · log 2 n) transitions suffice. For small alphabets, for instance if k = O(log 2 log 2 n), we further improve the upper bound to O(k 1+log * n · n). In particular, O(2 log * 2 n · n) transitions and hence almost linear size suffice for the binary alphabet! Finally we show the lower bound Ω(n · log 2 2 2k) and as a consequence the upper bound O(n · log 2 2 n) of [7] for general alphabets is best possible. Thus the conversion problem is solved for large alphabets (k = n Ω(1) ) and almost solved for small alphabets (k = O(1)).

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“…These operations in the set of automata reflect a more engineering, as in [2][3][4], than functional, as in [6,8], approach to the modeling of real methods for constructing discrete information processing devices. It is easy to verify that if a Moore automaton is the composition of Moore automata with feedback and output units, and in turn, each of components of the composition is a composition of some other Moore automata with other feedback and output units, then the first Moore automaton is a composition of these other Moore automata with some suitable feedback and output units.…”

Section: Composition Of Automatamentioning

confidence: 99%

“…For such class of compositions the most frequently are used the feedback of Moore automata and functional units without memory (switching circuits). It was found [2,3] the easily verifiable properties of the completeness of systems consisting of Moore automata and arbitrary switching circuits for socalled isomorphic realization (implementation up to the device memory structure). In [4] and later in [5] were formulated some verifiable sufficient conditions for the recognition of the completeness of systems consisting of Moore automata and arbitrary switching circuits for homomorphic realization (implementation up to the device behavior rather than to device memory structure).…”

Section: Introductionmentioning

confidence: 99%

Completeness Conditions of Systems of Moore Automata

Donis¹

2013

Information Technologies and Control

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The Abstract Theory of Automata

Cited by 394 publications

References 17 publications

The Inclusion Problem for Regular Expressions

The Inclusion Problem for Regular Expressions

Regular Expressions and NFAs Without ε-Transitions

Completeness Conditions of Systems of Moore Automata

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