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Complexity of equivalence relations and preorders from computability theory
[article]

2013
*
arXiv
*
pre-print

We study the relative

arXiv:1302.0580v2
fatcat:izdyprywmvccpis5rtcsk3n26q
*complexity**of**equivalence**relations**and**preorders**from**computability**theory**and**complexity**theory*. ... We show that Σ k*preorders*arising naturally in the above-mentioned areas are Σ k-complete. ... In this way we obtain some examples*of*natural Σ 0 n -complete*preorders**from**computability**theory*. ...##
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COMPLEXITY OF EQUIVALENCE RELATIONS AND PREORDERS FROM COMPUTABILITY THEORY

2014
*
Journal of Symbolic Logic (JSL)
*

We study the relative

doi:10.1017/jsl.2013.33
fatcat:niqu3gigufgg3i5yuuszxeom2m
*complexity**of**equivalence**relations**and**preorders**from**computability**theory**and**complexity**theory*. ... For us the*relations*will be on natural numbers,*and*f must be*computable*. We show that there is a ${\rm{\Pi }}_1^0$ -complete*equivalence**relation*, but no ${\rm{\Pi }}_k^0$ -complete for k ≥ 2. ... In this way we obtain some examples*of*natural Σ 0 n -complete*preorders**from**computability**theory*. ...##
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Equivalence Relations on Classes of Computable Structures
[chapter]

2009
*
Lecture Notes in Computer Science
*

We measure the

doi:10.1007/978-3-642-03073-4_21
fatcat:tkc2imruzrc2zg44ygekmrtoe4
*complexity**of*a description*of*K c or*of*an*equivalence**relation*on K c via the*complexity**of*the corresponding sets*of*indices. ... In the present paper we study the status*of*these Σ 1 1*equivalence**relations*(on classes*of**computable*structures with hyperarithmetical index set) within the class*of*Σ 1 1*equivalence**relations*as a ... One*of*the questions*of**computable*model*theory*is to study the algorithmic*complexity**of*such classes*of**computable*structures*and*various*relations*on these structures. ...##
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Page 4208 of Mathematical Reviews Vol. , Issue 99f
[page]

1999
*
Mathematical Reviews
*

[/O automata are encoded into the

*theory**of*testing*and*the reversed ‘must’*preorder*is shown to be*equivalent*to the quiescent*preorder*for strongly convergent, finitely branching I/O automata up to encoding ... Hromkovic, Communication*complexity**and*parallel*computing*, Springer, Berlin, 1997; MR 98f:68102] on the*complexity**of*spe- cific*computing*problems, which is one*of*the hardest tasks*of*recent theoretical ...##
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Comparing the isomorphism types of equivalence structures and preorders
[article]

2020
*
arXiv
*
pre-print

A general theme

arXiv:2001.08017v1
fatcat:ahhf3r4ovvgvldb5taj7tz5cie
*of**computable*structure*theory*is to investigate when structures have copies*of*a given*complexity*Γ. We discuss such problem for the case*of**equivalence*structures*and**preorders*. ... We show that there is a Π^0_1*equivalence*structure with no Σ^0_1 copy,*and*in fact that the isomorphism types realized by the Π^0_1*equivalence*structures coincide with those realized by the Δ^0_2*equivalence*... In recent times, following the work*of*Ng*and*Yu [16] , we initiated a systematic study*of*∆ 0 2*equivalence**relations*: we proved that*theory**of*ceers, co-ceers,*and*∆ 0 2*equivalence**relations*behave ...##
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On the Complexity of Deciding Behavioural Equivalences and Preorders. A Survey

1996
*
BRICS Report Series
*

This paper gives an overview

doi:10.7146/brics.v3i39.20021
fatcat:afzjm6bo5fhfhcl62e3ibyk7xe
*of*the*computational**complexity**of*all the*equivalences*in the linear/branching time hierarchy [vG90a]*and*the*preorders*<br />in the corresponding hierarchy*of**preorders*. ... For the class*of*BPP processes, all*preorders**and**equivalences*apart*from*bisimilarity are undecidable. ... Introduction Within concurrency*theory*, a number*of**preorders**and**equivalence**relations*between processes have been considered in various approaches to the semantics*of*concurrency*and*automatic verification ...##
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Page 5874 of Mathematical Reviews Vol. , Issue 98I
[page]

1998
*
Mathematical Reviews
*

Two processes E

*and*F are*related*(E C, F) if they have the same functionality (in this case, we have chosen strong bisimuilation*equivalence*)*and*E is at least as fast as F. ... Both the performance*preorder**and*the induced*equivalence*, called competitive*equivalence*, are provided with sound*and*com- plete axiomatizations for finite agents.” 98i1:68081 68Q10 68Q60 Fu, Yu Xi (PRC-JTU-EN ...##
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On Efficiency Preorders
[chapter]

2013
*
Lecture Notes in Computer Science
*

*Theories*

*of*efficiency

*preorders*

*and*precongruences for concurrent systems have been described in various papers. We describe a procedure to implement two

*of*these precongruences. ... Considering the extra information that is needed to be maintained while

*computing*efficiency

*preorders*, our procedure with a

*complexity*O(n 3 m), compares favourably with that for deciding observational ... Another important notion

*of*

*equivalence*is present by the automata

*theory*in

*computer*science. ...

##
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Page 1793 of Mathematical Reviews Vol. , Issue 85e
[page]

1985
*
Mathematical Reviews
*

One

*of*the first results is a characterization*of*P-selective sets in terms*of*polynomial time*computable**preorders**and*the*equivalence**relations**and*partial orderings that they induce. ... For a*preorder*R on £°*, define zSy if Ry*and*yRz,*and*define a binary*relation*R’ on £*/S by £R’7 if rRy, where Z denotes the*equivalence*class*of*z mod S. ...##
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Computable Component-wise Reducibility
[article]

2013
*
arXiv
*
pre-print

We consider

arXiv:1301.7112v1
fatcat:eqz3jivk3bfx3niz45gk6ofxuq
*equivalence**relations**and**preorders*complete for various levels*of*the arithmetical hierarchy under*computable*, component-wise reducibility. ... We show that implication in first order logic is a complete*preorder*for 1, the <^P_m*relation*on EXPTIME sets for 2*and*the embeddability*of**computable*subgroups*of*(,+) for 3. ... We choose to consider a*preorder**and*a resulting*equivalence**relation**from**complexity**theory*: that*of*polynomial time reducibility*of*EXPTIME sets. ...##
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Criteria for Homotopic Maps to be So Along Monotone Homotopies

2009
*
Electronical Notes in Theoretical Computer Science
*

The state spaces

doi:10.1016/j.entcs.2009.02.022
fatcat:fii3zaf7l5dkbh4zcg4zbcbdzu
*of*machines admit the structure*of*time. A homotopy*theory*respecting this additional structure can detect machine behavior unseen by classical homotopy*theory*. ... In an attempt to bootstrap classical tools into the world*of*abstract spacetime, we identify criteria for classically homotopic, monotone maps*of*pospaces to future homotope, or homotope along homotopies ... Acknowledgement The author thanks Eric Goubault*and*Emmanuel Haucourt for their helpful comments*and*suggestions. The author also thanks Zack Apoian, Steven Paulikas,*and*John Posch. ...##
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On the Complexity of Infinite Advice Strings

2018
*
International Colloquium on Automata, Languages and Programming
*

Turing machines)

doi:10.4230/lipics.icalp.2018.122
dblp:conf/icalp/Doueneau-Tabot18
fatcat:73yhszegivf5njr53nv3d54jga
*and*C a class*of*objects (e.g. languages), the*complexity**of*an infinite word α can be measured with respect to the amount*of*objects*from*C that are presentable with machines*from*M using ... This leads to several different classifications*of*infinite words that are studied in detail; we also derive logical*and**computational**equivalent*measures. ... An partial look on the 2WFT hierarchy*Equivalent*definitions for*preorders*over ω-words Greatest degree*of**computable*strings τ*Computable*strings Strings with decidable MSO-*theory*π A prime degree no ...##
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The Computational Complexity of Rationalizing Behavior

2010
*
Journal of Mathematical Economics
*

We study the

doi:10.1016/j.jmateco.2010.02.001
fatcat:2tunxm57fndqni5qesyfdsq5em
*complexity**of*rationalizing choice behavior. We do so by analyzing two polar cases,*and*a number*of*intermediate ones. ... We show that the task*of*finding the rationalizing complete*preorders*is*equivalent*to a graph problem. ... Furthermore, these binary*relations*define a problem in graph*theory*that is*equivalent*to the problem*of*rationalization. ...##
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On the Complexity of Rationalizing Behavior

2007
*
Social Science Research Network
*

We study the

doi:10.2139/ssrn.1015724
fatcat:trz6bgichbabjclfrxyvi5mjqu
*complexity**of*rationalizing choice behavior. We do so by analyzing two polar cases,*and*a number*of*intermediate ones. ... We show that the task*of*finding the rationalizing complete*preorders*is*equivalent*to a graph problem. ... Furthermore, these binary*relations*define a problem in graph*theory*that is*equivalent*to the problem*of*rationalization. ...##
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Complexity Issues for Preorders on Finite Labeled Forests
[chapter]

2011
*
Lecture Notes in Computer Science
*

Since G → (
Introduction Preliminaries The

doi:10.1007/978-3-642-21875-0_12
fatcat:6wohrblwznb4jhrcxtjtkhjkk4
*Complexity**of*≤ 0 The*Complexity**of*≤ 1 The*Complexity**of*≤ 2 The*Complexity**of*≤ 2 Theorem For any k < ω, the*relation*≤ 2 on F k is*computable*in time O(n ... The*relations*≤ 0 , ≤ 1 , ≤ 2 are*preorders*on F ω . It is easy to prove that any 0-morphism is a 1-morphism*and*any 1-morphism is a 2-morphism in turn. ...
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