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Application of formal languages in polynomial transformations of instances between NP-complete problems

Jorge A. Ruiz-Vanoye, Joaquín Pérez-Ortega, Rodolfo A. Pazos Rangel, Ocotlán Díaz-Parra, Héctor J. Fraire-Huacuja, Juan Frausto-Solís, Gerardo Reyes-Salgado, Laura Cruz-Reyes
2013 Journal of Zhejiang University SCIENCE C  
We propose the usage of formal languages for expressing instances of NP-complete problems for their application in polynomial transformations.  ...  In this paper we propose a methodology for transforming instances between NP-complete problems, which differs from Garey and Johnson's.  ...  In this paper, we propose the usage of formal languages to express instances of NP-complete problems for their application in polynomial transformations.  ... 
doi:10.1631/jzus.c1200349 fatcat:3oemuj5bunfqtduzuhnz5czsru

`` Strong '' NP-Completeness Results: Motivation, Examples, and Implications

M. R. Garey, D. S. Johnson
1978 Journal of the ACM  
The NP-completeness of a computational problem ~s frequently taken to unply its "mtractabthty" However, there are certain NP-complete problems mvolvmg numbers, such as PARTITION and KNAPSACK, which are  ...  In this paper we provide a standard framework for stating and proving "strong" NP-completeness results of this sort, survey some of the strong NP-completeness results proved to date, and indicate some  ...  A large number of people made useful comments based on a preliminary draft of this paper. Among these, we would especially like to thank  ... 
doi:10.1145/322077.322090 fatcat:cyw7tqo335gfvkowljdenowmby

Constructive complexity

Karl Abrahamson, Michael R. Fellows, Michael A. Langston, Bernard M.E. Moret
1991 Discrete Applied Mathematics  
Powerful and widely applicable, yet inherently nonconstructive, tools have recently become available for classifying decision problems as solvable in polynomial time, as a result of the work of Robertson  ...  These developments challenge the established view that equates tractability with polynomial-time solvability, since the existence of an inaccessible algorithm is of very little help in solving a problem  ...  However, in the following, we shall generally use the relational formalism explicitly; in that formalism, given relation 99, the set of acceptable instances of the problem is the domain of the relation  ... 
doi:10.1016/0166-218x(91)90074-7 fatcat:i6secoiuyrcb7g72tz62kb7v2y

Optimal Polynomial-Time Compression for Boolean Max CSP

Bart M. P. Jansen, Michał Włodarczyk, Peter Sanders, Grzegorz Herman, Fabrizio Grandoni
2020 European Symposium on Algorithms  
In the Boolean maximum constraint satisfaction problem - Max CSP(Γ) - one is given a collection of weighted applications of constraints from a finite constraint language Γ, over a common set of variables  ...  can be compressed into an equivalent instance with 𝒪(n^d log n) bits in polynomial time, 2) Max CSP(Γ) does not admit such a compression to 𝒪(n^{d-ε}) bits unless NP ⊆ co-NP / poly.  ...  Although we were able to get rid of the latter assumption in several cases, there is still a gap in this classification: does improving the running time for any degree-d Max CSP(Γ, N) imply an improvement  ... 
doi:10.4230/lipics.esa.2020.63 dblp:conf/esa/Jansen020 fatcat:vdmlgng22nebvltgqwmnfgmei4

Optimal polynomial-time compression for Boolean Max CSP [article]

Bart M.P. Jansen, Michał Włodarczyk
2020 arXiv   pre-print
In the Boolean maximum constraint satisfaction problem - Max CSP(Γ) - one is given a collection of weighted applications of constraints from a finite constraint language Γ, over a common set of variables  ...  An instance of Max CSP(Γ) can be compressed into an equivalent instance with O(n^dlog n) bits in polynomial time, 2.  ...  Conclusions and open problems We have provided a complete characterization of the optimal compression for Max CSP(Γ) in the case of a Boolean domain. a natural question arises about larger domains.  ... 
arXiv:2002.03443v1 fatcat:4yag7aw6tncytk4sa3jpbak7de

Reducibility and Completeness [chapter]

Eric Allender, Michael Loui, Kenneth Regan
1998 Algorithms and Theory of Computation Handbook  
Acknowledgments The first author was supported by the National Science Foundation under Grants CCF 0830133 and 0132787; portions of this work were performed while a visiting scholar at the Institute of  ...  Let A be a language in NP, and let f be a transformation function that reduces A to S in polynomial time t f (n).  ...  A problem is NP-complete in the strong sense if there is a fixed polynomial p such that for each instance x of the problem, the value of the largest number encoded in x is at most p(|x|).  ... 
doi:10.1201/9781420049503-c29 fatcat:v6gcv7iknrfprd3zquafahpevm

Complexities of the Centre and Median String Problems [chapter]

François Nicolas, Eric Rivals
2003 Lecture Notes in Computer Science  
Thus, it remains a crucial question whether the median string problem is NP-complete for finite and even binary alphabets.  ...  In the recent literature, one finds a theorem stating the NP-completeness of the median string for unbounded alphabets. However, in the above mentioned areas, the alphabet is often finite.  ...  Acknowledgment The authors thank Colin De La Higuera for reading a preliminary version of this work and Jens Gramm for introducing us to parameterized complexity.  ... 
doi:10.1007/3-540-44888-8_23 fatcat:ql3riru4ofe3xpzo72t6sbu7qe

Polynomial graph transformability

Hans-Jörg Kreowski, Sabine Kuske
2012 Theoretical Computer Science  
In this paper, we introduce and study polynomial graph transformability as a graphtransformational counterpart of the satisfiability problem of the propositional calculus.  ...  It is a known fact that an NP-problem is NP-complete if an NP-complete problem can be reduced to it.  ...  Hence, the two theorems above and the corollary yield the NP-completeness of polynomial graph transformability. Corollary 2. #nodesGT , sizeGT and PGT are NP-complete.  ... 
doi:10.1016/j.tcs.2011.12.039 fatcat:nh3wr4snbvdmvj5bp7dazprzw4

Computational consequences of agreement and ambiguity in natural language

Eric Sven Ristad, Robert C. Berwick
1989 Journal of Mathematical Psychology  
Note that T need not be in A? to be NP-hard. A problem is NP-complete if it is both in K? and NP-hard.  ...  A reduction converts instances of a problem T of known complexity into instances of a problem S whose complexity we wish to determine. The reduction operates in polynomial time.  ... 
doi:10.1016/0022-2496(89)90018-7 fatcat:vz4lqmqbyrgxjkd6knyqmhvlki

Computability vs. Nondeterministic and P vs. NP [article]

Jian-Ming Zhou
2013 arXiv   pre-print
This paper brings forth new concepts: NP (nondeterministic problem) and NP-algorithm (defined as the optimal algorithm to get the best fit approximation value of NP).  ...  Church-Turing Thesis that is equivalent of the Polynomial time and actual time; it redefines the NTM based on its undecidable set of its internal state.  ...  a transformer of same degree of facility has been reduced a judgment in the form of logic formal implication and gains the formal completeness.  ... 
arXiv:1305.4029v1 fatcat:yy6qt2g75fhj3fcb4mveymvqc4

Compilation Schemes: A Theoretical Tool for Assessing the Expressive Power of Planning Formalisms [chapter]

Bernhard Nebel
1999 Lecture Notes in Computer Science  
We formalize the intuition that expressive power is a measure of how concisely planning domains and plans can be expressed in a particular formalism by introducing the notion of \compilation schemes" between  ...  The recent approaches of extending the graphplan algorithm to handle more expressive planning formalisms raise the question of what the formal meaning of \expressive power" is.  ...  Acknowledgments The research reported in this paper was started and partly carried out while the author enjoyed being a visitor at the AI department of the University of New South Wales.  ... 
doi:10.1007/3-540-48238-5_15 fatcat:g46di72in5gqdb2kcewrw7jdfm

Conceptual Graphs Are Also Graphs [chapter]

Michel Chein, Marie-Laure Mugnier
2014 Lecture Notes in Computer Science  
Main topics of this paper are: a generalized formalism for simple CGs; a strong equivalence between CSP (Constraint Satisfaction Problem) and labelled graph morphism.  ...  The main objective of this paper is to add one more brick in building the CG model as a knowledge representation model autonomous from logic.  ...  Acknowledgements We thank Anne Preller for the example of Figure 4 , which shows the problems with individual markers in the proof of logical completeness.  ... 
doi:10.1007/978-3-319-08389-6_1 fatcat:fl47noysevherhmy4fcc4r6aua

The principle of optimality in the design of efficient algorithms

Paul Helman
1986 Journal of Mathematical Analysis and Applications  
Though there is almost certainly no algorithm that will run in polynomial time for all instances of an NP-complete problem, it may be that we can devise an algorithm that will run in polynomial time for  ...  The existence of a (deterministic) polynomial time algorithm for any NP-complete problem would imply the existence of a (deterministic) polynomial time algorithm for euery problem in NP (that is, P= NP  ...  ACKNOWLEDGMENT The author gratefully acknowledges the influence of Amon Rosenthal is helping to shape much of the perspective on dynamic programming that is found in this paper.  ... 
doi:10.1016/0022-247x(86)90147-2 fatcat:exktccbbcjgvdbnt56rop4tlti

P vs NP: P is Equal to NP: Desired Proof

Zulfia A. Chotchaeva
2021 Global Journal of Computer Science and Technology  
This paper presents proof of the equality of P and NP complexity classes when the NP problem is not harder to compute than to verify in polynomial time if we forget recursion that takes exponential running  ...  The paper's goal is to prove the existence of an algorithm solving the NP task in polynomial running time.  ...  Funding Information This research received no specific grant from any funding agency in the public, commercial, or notfor-profit sectors.  ... 
doi:10.34257/gjcstgvol21is3pg1 fatcat:qlnq76x6ynhshff3emt3o63ceq

Finding Solutions to NP Problems: Philosophical Difference Between Quantum and Evolutionary Search Algorithms [article]

G. W. Greenwood
2000 arXiv   pre-print
This paper uses instances of SAT, 3SAT and TSP to describe how these two methods differ in their approach to solving NP problems.  ...  There is no known polynomial-time algorithm that can solve an NP problem. Evolutionary search has been shown to be a viable method of finding acceptable solutions within a reasonable time period.  ...  in NP is polynomially reducible to P NP-complete problems are decision problems.  ... 
arXiv:quant-ph/0010021v1 fatcat:ho2jzdjms5hifi53ydmzmuxdpa
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