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Wednesday, July 29, 2020 | History

6 edition of The computational complexity of equivalence and isomorphism problems found in the catalog.

# The computational complexity of equivalence and isomorphism problems

## by Thomas Thierauf

Written in English

Subjects:
• Computational complexity -- Data processing,
• Isomorphisms (Mathematics) -- Data processing

• Edition Notes

Includes bibliographical references (p. [121]-130) and index.

Classifications The Physical Object Statement Thomas Thierauf. Series Lecture notes in computer science,, 1852 LC Classifications QA267.7 .T48 2000 Pagination viii, 135 p. ; Number of Pages 135 Open Library OL6898718M ISBN 10 3540410325 LC Control Number 00703237 OCLC/WorldCa 44937393

Computational Complexity: A Modern Approach Draft of a book: Dated January Comments welcome! Sanjeev Arora and Boaz Barak Princeton University [email protected] Not to be reproduced or distributed without the authors’ permission This is an Internet draft. Some chapters are more ﬁnished than others. References and.   We study the computational power of deciding whether a given truth-table can be described by a circuit of a given size (the Minimum Circuit Size Problem, or MCSP for short), and of the variant denoted as MKTP where circuit size is replaced by a polynomially-related Kolmogorov measure. All prior reductions from supposedly-intractable problems to MCSP / MKTP hinged on the power of .

About this book.   The graph isomorphism problem in general belongs to the class $\mathcal{N}$ but has not been proved to be in the class $\mathcal{NPC}$ or $\mathcal{P}$ and is of great interest in the study of computational complexity. See the surveys and and also Complexity theory.

To make the computational complexity consequences of the last two statements above precise, note that each of the polytopes ψ n and ψ n, n is uniquely determined by n, and so the input for either optimization problem max {〈 W, X 〉: X ∈ ψ n} or max {〈 W, X 〉: X ∈ ψ n, n} consists of n and an integer tensor W (see next section for. To determine if two lists of numbers are the same set, we sort both lists and see if we get the same result. The sorted list is a canonical form for the equivalence relation of set equality. Other canonical forms arise in graph isomorphism algorithms, and the equality of permutation groups given by generators. To determine if two graphs are cospectral (have the same eigenvalues), however, we.

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### The computational complexity of equivalence and isomorphism problems by Thomas Thierauf Download PDF EPUB FB2

The theory of computations is the study of the inherent difficulty of computational problems, that is, their computational complexity. This monograph analyzes the computational complexity of the satisfiability, equivalence, and almost-equivalence problems with respect to various computational.

The Computational Complexity of Equivalence and Isomorphism Problems (Lecture Notes in Computer Science ()) Paperback – August 4, by Thomas Thierauf (Author) › Visit Amazon's Thomas Thierauf Page.

Find all the books, read about the author, and more. See search Cited by: The Computational Complexity of Equivalence and Isomorphism Problems Book   January   with  5 Reads  How we measure 'reads' A 'read' is counted each time someone views a.

Get this from a library. The computational complexity of equivalence and isomorphism problems. [Thomas Thierauf]. We consider the question of when two games are equivalent and the computational complexity of deciding such a property for strategic games.

We introduce three types of isomorphisms depending on. Abstract. We study the computational complexity of the isomorphism and equivalence problems on systems of equations over a fixed finite group.

We show that the equivalence problem is in P if the group is Abelian, and coNP-complete if the group is by: 1. We propose this family as a reference framework for studying the computational complexity of fundamental graph problems.

To this purpose we characterize these classes using Cunningham decomposition and then use the devised structural characterization in order to show efficient algorithms for the recognition and isomorphism problems. Proceedings / [ed] Jirí Fiala, Václav Koubek and Jan Kratochvíl, Springer Berlin/Heidelberg,Vol.p.

Chapter in book (Refereed) Abstract [en] We study the computational complexity of the isomorphism and equivalence problems on systems of equations over a fixed finite group.

Complexity Classes of Equivalence Problems Revisited Lance Fortnow and Joshua A. Grochow Abstract To determine if two lists of numbers are the same set, we sort both lists and see if we get the same result.

The sorted list is a canonical form for the equivalence relation of set equality. Other canonical forms arise in graph isomorphism algorithms.

On the computational complexity of some classical equivalence relations on boolean functions. Theory Comput. Syst. v Google Scholar [6].

de Bruin, Game transformations and game equivalence. Technical Report X, IIL Technical Note, Google Scholar [7]. Casajus, A., Weak isomorphism of extensive games.

Home Browse by Title Books The graph isomorphism problem: its structural complexity The graph isomorphism problem: its structural complexity August August The graph isomorphism problem is the computational problem of determining whether two finite graphs are isomorphic.

The problem is not known to be solvable in polynomial time nor to be NP-complete, and therefore may be in the computational complexity class is known that the graph isomorphism problem is in the low hierarchy of class NP, which implies that it is not NP.

We investigate the computational complexity of the formula isomorphism problem (FI): on input of two boolean formulas F and G decide whether there exists a permutation of the variables of G such that F and G become equivalent. FI is contained in ${\Sigma_{2}{\bf P}}$, the second level of the polynomial hierarchy.

Our main result is a one-round interactive proof for the complementary formula. Computational complexity. Constructing the automorphism group is at least as difficult (in terms of its computational complexity) as solving the graph isomorphism problem, determining whether two given graphs correspond vertex-for-vertex andG and H are isomorphic if and only if the disconnected graph formed by the disjoint union of graphs G and H has an automorphism that.

The isomorphism problem admittedly gains its importance from a more theo-retical point of view. In complexity theory, isomorphism problems in general are notorious since often they resist a precise complexity theoretic classiﬁcation. Most famous of course is graph isomorphism, a candidate for an “intermediate problem” between P and the NP.

There are only a few known complexity results about isomorphism problems related to combinatorial t-designs: Prior to Spielman’s result for Steiner 2-designs, Miller [32] had shown that the specific case of isomorphism of line graphs derived from Steiner triple systems (i.e.

Steiner 2-designs with block size 3) can be determined in sub. We study the complexity of the isomorphism and automorphism problems for finite rings with unity. We show that both integer factorization and graph isomorphism reduce to the problem of counting automorphisms of rings. The problem is shown to be in the complexity class \\AMco\\AM and hence is not \\NP-complete unless the polynomial hierarchy collapses.

Integer [ ]. We investigate the complexity of ﬁnding prime implicants and minimum equiv-alent DNFs for Boolean formulas, and of testing equivalence and isomorphism of monotone formulas. For DNF related problems, the complexity of the monotone case diﬀers strongly from the arbitrary case.

We show that it is DP-complete to check. The Isomorphic Relation between sets is an equivalence relation. The Berman-Hartmanis conjecture is equivalent to saying that every NP-complete set is isomorphic to SAT.

The conjecture is still open though it has generated a considerable amount of research in computational complexity. But for now let me just explain why this question is. (English) In: Theoretical Computer Science, ISSNVol.noArticle in journal (Refereed) Published Abstract [en] We study the computational complexity of the isomorphism and equivalence problems on systems of equations over a fixed finite group.

In computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it. Particular focus is given to time and memory requirements. As the amount of resources required to run an algorithm generally varies with the size of the input, the complexity is typically expressed as a function n → f(n), where n is the size of the input and.CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Abstract.

We study the computational complexity of the isomorphism and equivalence problems on systems of equations over a fixed finite group. We show that the equivalence problem is in P if the group is Abelian, and coNP-complete if the group is non-Abelian.

We prove that if the group is non-Abelian, then the problem.CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): We investigate the computational complexity of the Boolean Isomorphism problem (BI): on input of two Boolean formulas F and G decide whether there exists a permutation of the variables of G such that F and G become equivalent.

Our main result is a one-round interactive proof for BI, where the verifier has .