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

Yijia Chen, Jörg Flum
2010 Lecture Notes in Computer Science  
We prove that TAUT has a 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).  ... 
doi:10.1007/978-3-642-14162-1_27 fatcat:edzvl2e3brcrfpfui2v4vk2s3y

And-parallel execution of logic programs on a shared-memory multiprocessor

Yow-Jian Lin, Vipin Kumar
1991 The Journal of Logic Programming  
The execution model is meant 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.  ... 
doi:10.1016/0743-1066(91)80003-v fatcat:q2czzi6fevhnbfqluxphpjb23m

Expressibility at the machine level versus structure level: ESO universal Horn Logic and the class P [article]

Prabhu Manyem
2012 arXiv   pre-print
We provide two 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.  ... 
arXiv:1106.4606v5 fatcat:sttu6s2o2be6pd2y7yxazeknmu

Bisimulation-invariant PTIME and higher-dimensional μ-calculus

Martin Otto
1999 Theoretical Computer Science  
It is also shown that higher-dimensional 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  ... 
doi:10.1016/s0304-3975(98)00314-4 fatcat:klwctsikb5fhpm45567db6vn6y

Consistent Query Answering: Five Easy Pieces [chapter]

Jan Chomicki
2006 Lecture Notes in Computer Science  
IC 2 build a 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.  ... 
doi:10.1007/11965893_1 fatcat:onj5d4mudfg3tkefdmbyrm4mge

Memoization for Unary Logic Programming: Characterizing PTIME [article]

Clément Aubert
2015 arXiv   pre-print
As an application of our techniques, we show a 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.  ... 
arXiv:1501.05104v2 fatcat:272rdzkgdjay5dozgcfuotkwym

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.”  ... 

On Slicewise Monotone Parameterized Problems and Optimal Proof Systems for TAUT [chapter]

Yijia Chen, Jörg Flum
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  ... 
doi:10.1007/978-3-642-15205-4_18 fatcat:4ge5ewg3graapmfn7fdqtvb5za

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

Yijia Chen, Jörg Flum, Moritz Müller
2013 Annals of Pure and Applied Logic  
Moreover, we characterize problems with an 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).  ... 
doi:10.1016/j.apal.2013.06.009 fatcat:7srp4nlblrfrbocrh2p3ngghou

Canonization for two variables and puzzles on the square

Martin Otto
1997 Annals of Pure and Applied Logic  
We consider infinitary 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.  ... 
doi:10.1016/s0168-0072(96)00047-4 fatcat:ezv2uqeasjgwljsddviacuzium

On the Complexity of Query Result Diversification

Ting Deng, Wenfei Fan
2014 ACM Transactions on Database Systems  
Query result diversification is a bi-criteria 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  ... 
doi:10.1145/2602136 fatcat:a5t4c5nsujhtvfs3p2k35vsxhu

Consistency and Optimality [chapter]

Yijia Chen, Jörg Flum, Moritz Müller
2011 Lecture Notes in Computer Science  
Moreover, we characterize problems with an 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).  ... 
doi:10.1007/978-3-642-21875-0_7 fatcat:6kplv3ezmvgwrg7gpwq5jib7ie

On the complexity of query result diversification

Ting Deng, Wenfei Fan
2013 Proceedings of the VLDB Endowment  
Query result diversification is a bi-criteria 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  ... 
doi:10.14778/2536354.2536358 fatcat:mrsuoyqjmvfq3dtmemkv333ssm

Regular path queries with constraints

Serge Abiteboul, Victor Vianu
1997 Proceedings of the sixteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems - PODS '97  
In particular, decidability 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.  ... 
doi:10.1145/263661.263676 dblp:conf/pods/AbiteboulV97 fatcat:ur4y3vrwevdm3p3dz2c6dgpsee
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