Infinite-word languages and continuous mappings

Redziejowski, Roman R.

doi:10.1016/0304-3975(86)90166-0

Cited by 16 publications

(16 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This generalises the corresponding definition for infinite words or streams in [55,60,61,65,66] (to cite just a few), which is based on [20]. Other notations for lim P found in the literature are P δ or P .…”

Section: An Alternative Characterisation Of Infinite Idealsmentioning

confidence: 67%

“…Concerning the underlying theory, our domain-theoretic notions should be tied in more closely with the topological view (see eg. [55,59]). Moreover, in the stream domain there obviously is a close connection with temporal operators: str P is related to intermittent assertions [15] and hence the formula PQP (always eventually P ) in temporal logic, while saf P corresponds to i P (P holds in all initial subintervals [48]).…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Ideal Stream Algebra

Möller

1998

Prospects for Hardware Foundations

View full text Add to dashboard Cite

Section: An Alternative Characterisation Of Infinite Idealsmentioning

confidence: 67%

Section: Resultsmentioning

confidence: 99%

Ideal Stream Algebra

Möller

1998

Prospects for Hardware Foundations

View full text Add to dashboard Cite

“…A different approach to defining a natural topology on X ∞ is proposed in [50]. We refer to this topology as τ R .…”

Section: Redziejowski's Topologymentioning

confidence: 99%

Topology on words

Calude¹,

Jürgensen²,

Staiger³

2009

Theoretical Computer Science

View full text Add to dashboard Cite

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.

show abstract

“…Infinite strings (words) can be considered [9] as limits of finite words and topology as a theoretical study of limits. Languages with infinite strings have been studied as subsets of a topological space.…”

Section: Introductionmentioning

confidence: 99%

Topological Properties of Parallel Series Language

Mohana.¹,

Desikan²,

Dare³

2019

IJRTE

View full text Add to dashboard Cite

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.

show abstract

Infinite-word languages and continuous mappings

Cited by 16 publications

References 21 publications

Ideal Stream Algebra

Ideal Stream Algebra

Topology on words

Topological Properties of Parallel Series Language

Contact Info

Product

Resources

About