Subword topology

Dare, V. R.; Siromoney, Rani

doi:10.1016/0304-3975(86)90143-x

Cited by 3 publications

(6 citation statements)

References 2 publications

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“…For the infix order, Dare and Siromoney [16] obtained the identity cl [16] is a special case of Theorem 42.…”

Section: Adherences Related To the Topologies τ ≤mentioning

confidence: 94%

“…The topology τ (ω) ≤ i , also known as the subword topology, was investigated in [16,60]. To study it, the following notion of disjunctivity is useful.…”

Section: Subword Topology and Disjunctive ω-Wordsmentioning

confidence: 99%

“…The investigation of the topology τ (ω) ≤ e induced by the embedding order can be carried out in a manner analogous to the subword topology (see also [16]). Here the ω-words containing each letter a ∈ X infinitely often play the same rôle as the disjunctive words in the case of the subword topology.…”

Section: Embedding Ordermentioning

confidence: 99%

“…Adherence (or ls-limit) was first introduced for the prefix relation ≤ p (see [57,61,38,42,4,58,59]), and then in [16] for the infix order ≤ i .…”

Section: Adherences Related To the Topologies τ ≤mentioning

confidence: 99%

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Topology on words

Calude¹,

Jürgensen²,

Staiger³

2009

Theoretical Computer Science

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Order-based topologies a b s t r a c tWe investigate properties of topologies on sets of finite and infinite words over a finite alphabet. The guiding example is the topology generated by the prefix relation on the set of finite words, considered as a partial order. This partial order extends naturally to the set of infinite words; hence it generates a topology on the union of the sets of finite and infinite words. We consider several partial orders which have similar properties and identify general principles according to which the transition from finite to infinite words is natural. We provide a uniform topological framework for the set of finite and infinite words to handle limits in a general fashion.

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“…For the infix order, Dare and Siromoney [16] obtained the identity cl [16] is a special case of Theorem 42.…”

Section: Adherences Related To the Topologies τ ≤mentioning

confidence: 94%

“…The topology τ (ω) ≤ i , also known as the subword topology, was investigated in [16,60]. To study it, the following notion of disjunctivity is useful.…”

Section: Subword Topology and Disjunctive ω-Wordsmentioning

confidence: 99%

Section: Embedding Ordermentioning

confidence: 99%

“…Adherence (or ls-limit) was first introduced for the prefix relation ≤ p (see [57,61,38,42,4,58,59]), and then in [16] for the infix order ≤ i .…”

Section: Adherences Related To the Topologies τ ≤mentioning

confidence: 99%

See 2 more Smart Citations

Topology on words

Calude¹,

Jürgensen²,

Staiger³

2009

Theoretical Computer Science

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“…A deep analysis shows that the notion of limit generated by the natural topology is different from that used in the theory of ω-automata. Concepts of limit associated with a topology have been studied in [1,2,3,5,6] limit point is the most important concept. Kuroda [7] has shown that it is possible to handle problems regarding syntactic analysis and translation using topological methods and concepts.…”

Section: Introductionmentioning

confidence: 99%

Topological Properties of Parallel Series Language

Mohana.¹,

Desikan²,

Dare³

2019

IJRTE

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Parallelism is a process by which a sequential string is broken down into a number of alphabets and used to speed up the acceptance of a string. To identify the parallelisable string, we have used parallel operator || and defined the language as parallel series languages. Algebraic and recognition properties of series parallel posets have been studied by Lodaya in [8]. In this paper, we have introduced finite and infinite parallel series language (parallel strings are connected sequentially). We have considered the set of all parallel series language as topological space and prefix order relation (poset relation) has been used to relate two parallel series strings. Topological concepts like limit, sequence, open set, closed set and basis for parallel series languages and their properties have been derived.

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Determining and stationary sets for some classes of partial recursive functions

Calude¹,

Istrate²

1991

Theoretical Computer Science

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Subword topology

Cited by 3 publications

References 2 publications

Topology on words

Topology on words

Topological Properties of Parallel Series Language

Determining and stationary sets for some classes of partial recursive functions

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