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

2013
*
Journal of Zhejiang University SCIENCE C
*

We propose the usage

doi:10.1631/jzus.c1200349
fatcat:3oemuj5bunfqtduzuhnz5czsru
*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*. ...##
###
`` Strong '' NP-Completeness Results: Motivation, Examples, and Implications

1978
*
Journal of the ACM
*

The

doi:10.1145/322077.322090
fatcat:cyw7tqo335gfvkowljdenowmby
*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 ...##
###
Constructive complexity

1991
*
Discrete Applied Mathematics
*

Powerful and widely

doi:10.1016/0166-218x(91)90074-7
fatcat:i6secoiuyrcb7g72tz62kb7v2y
*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 ...##
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Optimal Polynomial-Time Compression for Boolean Max CSP

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 ...

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

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. ...

##
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Reducibility and Completeness
[chapter]

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

doi:10.1201/9781420049503-c29
fatcat:v6gcv7iknrfprd3zquafahpevm
*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|). ...##
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Complexities of the Centre and Median String Problems
[chapter]

2003
*
Lecture Notes in Computer Science
*

Thus, it remains a crucial question whether the median string

doi:10.1007/3-540-44888-8_23
fatcat:ql3riru4ofe3xpzo72t6sbu7qe
*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. ...##
###
Polynomial graph transformability

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*. ...

##
###
Computational consequences of agreement and ambiguity in natural language

1989
*
Journal of Mathematical Psychology
*

Note that T need not be

doi:10.1016/0022-2496(89)90018-7
fatcat:vz4lqmqbyrgxjkd6knyqmhvlki
*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. ...##
###
Computability vs. Nondeterministic and P vs. NP
[article]

2013
*
arXiv
*
pre-print

This paper brings forth new concepts:

arXiv:1305.4029v1
fatcat:yy6qt2g75fhj3fcb4mveymvqc4
*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*. ...##
###
Compilation Schemes: A Theoretical Tool for Assessing the Expressive Power of Planning Formalisms
[chapter]

1999
*
Lecture Notes in Computer Science
*

We

doi:10.1007/3-540-48238-5_15
fatcat:g46di72in5gqdb2kcewrw7jdfm
*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. ...##
###
Conceptual Graphs Are Also Graphs
[chapter]

2014
*
Lecture Notes in Computer Science
*

Main topics

doi:10.1007/978-3-319-08389-6_1
fatcat:fl47noysevherhmy4fcc4r6aua
*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*. ...##
###
The principle of optimality in the design of efficient algorithms

1986
*
Journal of Mathematical Analysis and Applications
*

Though there is almost certainly no algorithm that will run

doi:10.1016/0022-247x(86)90147-2
fatcat:exktccbbcjgvdbnt56rop4tlti
*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. ...##
###
P vs NP: P is Equal to NP: Desired Proof

2021
*
Global Journal of Computer Science and Technology
*

This paper presents proof

doi:10.34257/gjcstgvol21is3pg1
fatcat:qlnq76x6ynhshff3emt3o63ceq
*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. ...##
###
Finding Solutions to NP Problems: Philosophical Difference Between Quantum and Evolutionary Search Algorithms
[article]

2000
*
arXiv
*
pre-print

This paper uses

arXiv:quant-ph/0010021v1
fatcat:ho2jzdjms5hifi53ydmzmuxdpa
*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*. ...
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