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

Egor Ianovski, Keng Meng Ng, Russell Miller, Andre Nies
2013 arXiv   pre-print
We study the relative 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.  ... 
arXiv:1302.0580v2 fatcat:izdyprywmvccpis5rtcsk3n26q

COMPLEXITY OF EQUIVALENCE RELATIONS AND PREORDERS FROM COMPUTABILITY THEORY

EGOR IANOVSKI, RUSSELL MILLER, KENG MENG NG, ANDRÉ NIES
2014 Journal of Symbolic Logic (JSL)  
We study the relative 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.  ... 
doi:10.1017/jsl.2013.33 fatcat:niqu3gigufgg3i5yuuszxeom2m

Equivalence Relations on Classes of Computable Structures [chapter]

Ekaterina B. Fokina, Sy-David Friedman
2009 Lecture Notes in Computer Science  
We measure the 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.  ... 
doi:10.1007/978-3-642-03073-4_21 fatcat:tkc2imruzrc2zg44ygekmrtoe4

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  ... 

Comparing the isomorphism types of equivalence structures and preorders [article]

Nikolay Bazhenov, Luca San Mauro
2020 arXiv   pre-print
A general theme 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  ... 
arXiv:2001.08017v1 fatcat:ahhf3r4ovvgvldb5taj7tz5cie

On the Complexity of Deciding Behavioural Equivalences and Preorders. A Survey

Hans Hüttel, Sandeep Shukla
1996 BRICS Report Series  
This paper gives an overview 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  ... 
doi:10.7146/brics.v3i39.20021 fatcat:afzjm6bo5fhfhcl62e3ibyk7xe

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  ... 

On Efficiency Preorders [chapter]

Manish Gaur, S. Arun-Kumar
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.  ... 
doi:10.1007/978-3-642-40213-5_6 fatcat:cwsz7tsvnvfrbgnqehhpaw6xqq

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.  ... 

Computable Component-wise Reducibility [article]

Egor Ianovski
2013 arXiv   pre-print
We consider 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.  ... 
arXiv:1301.7112v1 fatcat:eqz3jivk3bfx3niz45gk6ofxuq

Criteria for Homotopic Maps to be So Along Monotone Homotopies

Sanjeevi Krishnan
2009 Electronical Notes in Theoretical Computer Science  
The state spaces 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.  ... 
doi:10.1016/j.entcs.2009.02.022 fatcat:fii3zaf7l5dkbh4zcg4zbcbdzu

On the Complexity of Infinite Advice Strings

Gaëtan Douéneau-Tabot, Michael Wagner
2018 International Colloquium on Automata, Languages and Programming  
Turing machines) 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  ... 
doi:10.4230/lipics.icalp.2018.122 dblp:conf/icalp/Doueneau-Tabot18 fatcat:73yhszegivf5njr53nv3d54jga

The Computational Complexity of Rationalizing Behavior

Jose Apesteguia, Miguel A. Ballester
2010 Journal of Mathematical Economics  
We study the 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.  ... 
doi:10.1016/j.jmateco.2010.02.001 fatcat:2tunxm57fndqni5qesyfdsq5em

On the Complexity of Rationalizing Behavior

Jose Apesteguia, Miguel A. Ballester
2007 Social Science Research Network  
We study the 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.  ... 
doi:10.2139/ssrn.1015724 fatcat:trz6bgichbabjclfrxyvi5mjqu

Complexity Issues for Preorders on Finite Labeled Forests [chapter]

Peter Hertling, Victor Selivanov
2011 Lecture Notes in Computer Science  
Since G → ( Introduction Preliminaries The 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.  ... 
doi:10.1007/978-3-642-21875-0_12 fatcat:6wohrblwznb4jhrcxtjtkhjkk4
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