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On p-Optimal Proof Systems and Logics for PTIME
[chapter]

2010
*
Lecture Notes in Computer Science
*

We prove that TAUT has a

doi:10.1007/978-3-642-14162-1_27
fatcat:edzvl2e3brcrfpfui2v4vk2s3y
*p*-*optimal**proof**system*if*and*only if a*logic*related to least fixed-point*logic*captures polynomial time*on*all finite structures. ... Furthermore, we show that TAUT has no effectively*p*-*optimal**proof**system*if NTIME(h O(1) ) ⊆ DTIME(h O(log h) )*for*every time constructible*and*increasing function h. ... Acknowledgement This research has been partially supported by the National Nature Science Foundation of China (60970011)*and*the Sino-German Center*for*Research Promotion (GZ400). ...##
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And-parallel execution of logic programs on a shared-memory multiprocessor

1991
*
The Journal of Logic Programming
*

The execution model is meant

doi:10.1016/0743-1066(91)80003-v
fatcat:q2czzi6fevhnbfqluxphpjb23m
*for**logic*programs with "don't-know nondeterrninism",*and*handles binding conflicts by dynamically detecting dependencies among literals. ... t> This paper presents the implementation*and*performance results of an ANn-parallel execution model of*logic*programs*on*a shared-memory multiprocessor. ... The authors would like to thank Manuel Hermenegildo*for*many useful discussions. ...##
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Expressibility at the machine level versus structure level: ESO universal Horn Logic and the class P
[article]

2012
*
arXiv
*
pre-print

We provide two

arXiv:1106.4606v5
fatcat:sttu6s2o2be6pd2y7yxazeknmu
*proofs*---*one*based*on*reduced products of two structures,*and*another based*on*approximability theory (the second*proof*is under the assumption that*P*is not the same as NP). ... We show that ESO universal Horn*logic*(existential second*logic*where the first order part is a universal Horn formula) is insufficient to capture*P*, the class of problems decidable in polynomial time. ...*Proof*based*on*approximation theory Here we provide another*proof*of Theorem 20, under the assumption that*P*= NP. ...##
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Bisimulation-invariant PTIME and higher-dimensional μ-calculus

1999
*
Theoretical Computer Science
*

It is also shown that higher-dimensional

doi:10.1016/s0304-3975(98)00314-4
fatcat:klwctsikb5fhpm45567db6vn6y
*p*-calculus is undecidable*for*satisfiability in finite structures,*and*even Et-hard over general structures. ... Bisimulation-invariant*PTIME*, or the modal fragment of*PTIME*, thus proves to be*one*of the very rare cases in which a*logical*characterization is known in a setting of unordered structures. ... Just as a natural*logic**for**PTIME*would, if it exists, be the theoretically ideal database language in the world of relational databases, the higher-dimensional*p*-calculus is, in a precise sense, an*optimal*...##
###
Consistent Query Answering: Five Easy Pieces
[chapter]

2006
*
Lecture Notes in Computer Science
*

IC 2 build a

doi:10.1007/11965893_1
fatcat:onj5d4mudfg3tkefdmbyrm4mge
*logic*program*P*Q expressing Q 3 use a*logic*programming*system*that computes the query atoms present in all models of*P*IC ,D ∪*P*Q . ... find a consistent set of facts S such that • S ⊇ {*P*1 (t 1 ), . . . ,*P*m (t m )} •*for*every fact A ∈ {*P*m+1 (t m+1 ), . . . ,*P*n (t n )}: A ∈ D*Proof*. ...##
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Memoization for Unary Logic Programming: Characterizing PTIME
[article]

2015
*
arXiv
*
pre-print

As an application of our techniques, we show a

arXiv:1501.05104v2
fatcat:272rdzkgdjay5dozgcfuotkwym
*PTIME*-completeness result*for*a class of*logic*programming queries which use only unary function symbols. ... We then introduce an algebraic counterpart of the memoization technique in order to show its*PTIME*soundness. We finally relate our approach*and*complexity results to complexity of*logic*programming. ... By restricting the rules of the*logical**system*,*one*obtains a subsystem where less*proofs*of type Nat ⇒ Nat can be written, hence less algorithms can be represented. ...##
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Page 7279 of Mathematical Reviews Vol. , Issue 98K
[page]

1998
*
Mathematical Reviews
*

Oracle machines are introduced along with a statement of,

*and*sketch of a*proof**for*, the Baker/Gill/Solovay theorem*on*the slipperiness of applying relativization to the*P*= NP problem. ... This result is*optimal*in the sense that four rounds*and*a*one*-way function are each individually necessary to achieve a negligible error zero-knowledge argument*for*NP.” ...##
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On Slicewise Monotone Parameterized Problems and Optimal Proof Systems for TAUT
[chapter]

2010
*
Lecture Notes in Computer Science
*

*For*a reasonable sound

*and*complete

*proof*calculus

*for*first-order

*logic*consider the problem to decide, given a sentence ϕ of first-order

*logic*

*and*a natural number n, whether ϕ has no

*proof*of length ... We show that there is a nondeterministic algorithm accepting this problem which,

*for*fixed ϕ, has running time bounded by a polynomial in n if

*and*only if there is an

*optimal*

*proof*

*system*

*for*the set TAUT ... This research has been partially supported by the National Nature Science Foundation of China (60970011), the Sino-German Center

*for*Research Promotion (GZ400),

*and*the John Templeton Foundation through ...

##
###
Page 8370 of Mathematical Reviews Vol. , Issue 2000m
[page]

2000
*
Mathematical Reviews
*

(

*For*example, the sketch*on**p*. 278 of Cantor’s*proof*that a perfect set has the power of the continuum is defective,*and*the*proof*of Cantor’s theorem*on**p*. 287 has an unnecessary use of the trichotomy ... The open question of whether there can be a*logic*which captures*PTIME**on*arbitrary structures is clearly introduced*and*explained. ...##
###
Consistency, optimality, and incompleteness

2013
*
Annals of Pure and Applied Logic
*

Moreover, we characterize problems with an

doi:10.1016/j.apal.2013.06.009
fatcat:7srp4nlblrfrbocrh2p3ngghou
*optimal*algorithm in terms of arithmetical theories. ... We characterize T ∪ {ConT } as the minimal extension of T proving*for*some algorithm that it decides P0 as fast as any algorithm B with the property that T proves that B decides P0. ... Yijia Chen is affiliated with BASICS*and*MOE-MS Key Laboratory*for*Intelligent Computing*and*Intelligent*Systems*which is supported by National Nature Science Foundation of China (61033002). ...##
###
Canonization for two variables and puzzles on the square

1997
*
Annals of Pure and Applied Logic
*

We consider infinitary

doi:10.1016/s0168-0072(96)00047-4
fatcat:ezv2uqeasjgwljsddviacuzium
*logic*with only two variable symbols, both with*and*without counting quantifiers, i.e. L* := L&,*and*C2 := L~,(3'm),E,. ... The main result is that finite relational structures admit*PTIME*canonization with respect to L2*and*C2: there are polynomial time computable fimctors mapping finite relational structures to unique representatives ... See [23]*for*more*on*the role of the Lk*and*[24]*on*their relation with fixed-point*logics*. ...##
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On the Complexity of Query Result Diversification

2014
*
ACM Transactions on Database Systems
*

Query result diversification is a bi-criteria

doi:10.1145/2602136
fatcat:a5t4c5nsujhtvfs3p2k35vsxhu
*optimization*problem*for*ranking query results. ... We study these problems*for*a variety of query languages*and**for*three objective functions. ...*For*the upper bound, we show that it is in*PTIME*to verify whether a given set U is a valid set*for*fixed Q in FO, by the definition of #*P*(i.e., #·*P*). (2) When F (·) is Fmono(·), the*proof*is more involved ...##
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Consistency and Optimality
[chapter]

2011
*
Lecture Notes in Computer Science
*

Moreover, we characterize problems with an

doi:10.1007/978-3-642-21875-0_7
fatcat:6kplv3ezmvgwrg7gpwq5jib7ie
*optimal*algorithm in terms of arithmetical theories. ...*For*theories T containing a sufficiently rich part of true arithmetic we characterize T ∪ {ConT } as the minimal extension of T proving*for*some algorithm that it decides Q0 as fast as any algorithm B ... Yijia Chen is affiliated with BASICS*and*MOE-MS Key Laboratory*for*Intelligent Computing*and*Intelligent*Systems*which is supported by National Nature Science Foundation of China (61033002). ...##
###
On the complexity of query result diversification

2013
*
Proceedings of the VLDB Endowment
*

Query result diversification is a bi-criteria

doi:10.14778/2536354.2536358
fatcat:mrsuoyqjmvfq3dtmemkv333ssm
*optimization*problem*for*ranking query results. ... We study these problems*for*a variety of query languages*and**for*three objective functions. ...*For*the upper bound, we show that it is in*PTIME*to verify whether a given set U is a valid set*for*fixed Q in FO, by the definition of #*P*(i.e., #·*P*). (2) When F (·) is Fmono(·), the*proof*is more involved ...##
###
Regular path queries with constraints

1997
*
Proceedings of the sixteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems - PODS '97
*

In particular, decidability

doi:10.1145/263661.263676
dblp:conf/pods/AbiteboulV97
fatcat:ur4y3vrwevdm3p3dz2c6dgpsee
*and*complexity results*on*the implication problem*for*path constraints are established. ... The focus is*on*the use of local information expressed in the form of path constraints in the*optimization*of path expression queries. ... This problem lies at the confluence of language theory, rewriting*systems*,*and**logic*. ...
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