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In [[theoretical computer science]], '''stuttering equivalence''',<ref>{{cite book | first1 = Jan Friso | last1 = Groote | first2 = Frits W. | last2 = Vaandrager | url = http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.140.1834 | chapter = An efficient algorithm for branching bisimulation and stuttering equivalence | title = Proceedings of the 17th International Colloquium on Automata, Languages and Programming | editor1-first = Michael S. | editor1-last = Paterson | publisher = [[Springer-Verlag]] | series = [[Lecture Notes in Computer Science]] | volume = 443 | pages = 626–638 | year = 1990 | isbn = 0-387-52826-1 | doi = 10.1007/BFb0032063 }}</ref> a relation written as | |||
[[Image:Stuttering Equivalence.pdf|thumb|The paths <math>\pi</math> and <math>\pi'</math> are stuttering equivalent.]] | |||
:<math>\pi\sim_{st}\pi'</math>, | |||
can be seen as a partitioning of path <math>\pi</math> and <math>\pi'</math> into blocks, so that states in the <math>k^{\mathrm{th}}</math> block of one path are labeled (<math>L(\sdot)</math>) the same as states in the <math>k^{\mathrm{th}}</math> block of the other path. Corresponding blocks may have different lengths. | |||
Formally, this can be expressed as two infinite paths <math>\pi=s_0, s_1, \ldots</math> and <math>\pi'=r_0, r_1, \ldots</math> which are stuttering equivalent (<math>\pi \sim_{st} \pi'</math>) if there are two infinite sequences of integers <math>0 = i_0 < i_1 < i_2 < \ldots</math> and <math>0 = j_0 < j_1 < j_2 < \ldots</math> such that for every block <math>k \geq 0</math> holds <math>L(s_{i_k}) = L(s_{i_k+1}) = \ldots = L(s_{i_{k+1}-1}) = L(r_{j_k}) = L(r_{j_k+1}) = \ldots = L(r_{j_{k+1}-1})</math>. | |||
Stuttering equivalence is not the same as [[bisimulation]], since bisimulation cannot capture the semantics of the 'eventually' (or 'finally') operator found in [[Linear temporal logic|linear temporal]]/[[Computation tree logic|computation tree logic(branching time logic)]]([[modal logic]]). So-called ''branching bisimulation'' has to be used.{{Citation needed|date=April 2012}} | |||
==References== | |||
{{reflist}} | |||
[[Category:Formal methods]] | |||
[[Category:Logic in computer science]] | |||
{{Comp-sci-theory-stub}} | |||
Latest revision as of 16:38, 4 January 2014
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In theoretical computer science, stuttering equivalence,[1] a relation written as
can be seen as a partitioning of path and into blocks, so that states in the block of one path are labeled () the same as states in the block of the other path. Corresponding blocks may have different lengths.
Formally, this can be expressed as two infinite paths and which are stuttering equivalent () if there are two infinite sequences of integers and such that for every block holds .
Stuttering equivalence is not the same as bisimulation, since bisimulation cannot capture the semantics of the 'eventually' (or 'finally') operator found in linear temporal/computation tree logic(branching time logic)(modal logic). So-called branching bisimulation has to be used.Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park.
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