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Unary Resolution: Characterizing Ptime
[chapter]
<span title="">2016</span>
<i title="Springer Berlin Heidelberg">
<a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a>
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We give a characterization of deterministic polynomial time computation based on an algebraic structure called the resolution semiring (whose elements can be understood as logic programs or sets of rewriting ...
As a direct consequence, we get a Ptime-completeness result for a class of logic programming queries that uses only unary function symbols. ...
Our main contribution here is a characterization of the class Ptime by studying a natural restriction, namely that one is allowed to use exclusively unary function symbols. ...
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Memoization for Unary Logic Programming: Characterizing PTIME
[article]
<span title="2015-02-04">2015</span>
<i >
arXiv
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<span class="release-stage" >pre-print</span>
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<span title="2015-01-21">2015</span>
<span class="release-stage" >pre-print</span>
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1501.05104v1">arXiv:1501.05104v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tsnoi2edcrd5xcvbt64t6frx7m">fatcat:tsnoi2edcrd5xcvbt64t6frx7m</a> </span>
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We give a characterization of deterministic polynomial time computation based on an algebraic structure called the resolution semiring, whose elements can be understood as logic programs or sets of rewriting ...
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. ...
Our main contribution here is a characterization of the class PTIME by studying a natural restriction, namely that one is allowed to use exclusively unary function symbols. ...
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On The Resolution Semiring
<span title="2014-12-04">2014</span>
<i title="Zenodo">
Zenodo
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programs.Secondly, complexity theory problematics will be considered: while thenilpotency problem in the semiring we study is undecidable in general, it willappear that certain restrictions allow for characterizations ...
More specifically, let us mention classical work on implicit characterizations of the complexity classes we study in this thesis: As for Ptime, characterizations have been obtained as restrictions on recursion ...
We explore their algebraic properties related to the notion of nilpotency, which will be used as an acceptance condition when characterizing the complexity classes Logspace, NLogspace and Ptime. ...
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Automated theorem proving by resolution in non-classical logics
<span title="2007-06-13">2007</span>
<i title="Springer Nature">
<a target="_blank" rel="noopener" href="https://fatcat.wiki/container/j2td7x4trvgx7pjoienrccryxq" style="color: black;">Annals of Mathematics and Artificial Intelligence</a>
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This paper is an overview of a variety of results, all centered around a common theme, namely embedding of non-classical logics into first order logic and resolution theorem proving. ...
In this context, we show that refinements of resolution can often be used successfully for automated theorem proving, and in many interesting cases yield optimal decision procedures. ...
For every rôle name R, we introduce two unary function symbols, f ∃R and f ∀R . ...
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Parameter Compilation
[article]
<span title="2015-03-01">2015</span>
<i >
arXiv
</i>
<span class="release-stage" >pre-print</span>
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In resolving instances of a computational problem, if multiple instances of interest share a feature in common, it may be fruitful to compile this feature into a format that allows for more efficient resolution ...
Here, by a unary signature, we mean a signature containing only unary relation symbols. ...
From the just-given characterization of chopped-C, we may infer the following two results. Proposition 15. ...
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Page 6722 of Mathematical Reviews Vol. , Issue 2004i
[page]
<span title="">2004</span>
<i title="American Mathematical Society">
<a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a>
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Restricting the induction rule to £; formulas one gets instead the class E> of Grzegorezyk, or alternatively the PTIME functions (depending on whether one works with unary or binary notation). ...
Bellantoni and Cook (1992) gave a syntactic characterization of the complexity class PTIME via a simple syntactic restriction of the scheme of primitive recursion, obtained by separating the variables ...
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On Partial Features in the $$\mathcal{DLF}$$ Family of Description Logics
[chapter]
<span title="">2016</span>
<i title="Springer International Publishing">
<a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a>
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The DLF dialects of description logic are fragments of first order logic with underlying signatures based on unary predicate symbols and on unary function symbols interpreted as total functions. ...
In earlier work, we have shown how computational properties of logical consequence for dialects of this family without inverse features are preserved when unary function symbols are interpreted instead ...
Pf | Pf is a prefix of a path expression in Q and Pf is a feature occurring in T or id }, write C C to denote unary predicates for C ∈ CON(T , Q), and introduce a unary predicate D and a binary predicate ...
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Ontology-Based Data Access
<span title="2014-12-30">2014</span>
<i title="Association for Computing Machinery (ACM)">
<a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ahla23r2jva2bp2hlkt5rtbx4y" style="color: black;">ACM Transactions on Database Systems</a>
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database queries are given as some form of conjunctive query and the ontologies are formulated in description logics or other relevant fragments of first-order logic, such as the guarded fragment and the unary ...
and CONP unless PTIME = NP. ...
Consequently, (ALCF, AQ) does not have a dichotomy between PTIME and CONP (unless PTIME = NP). ...
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Understanding the Complexity of Lifted Inference and Asymmetric Weighted Model Counting
[article]
<span title="2014-07-29">2014</span>
<i >
arXiv
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<span title="2014-05-13">2014</span>
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; we prove that, in the first case our algorithm solves the WFOMC problem in PTIME, and in the second case it fails. ...
Second, we provide a novel dichotomy result for a non-trivial fragment of FO CNF sentences, showing that for each sentence the WFOMC problem is either in PTIME or #P-hard in the size of the input domain ...
The search for D 1 , D 2 can proceed using some standard inference algorithm, e.g. resolution. ...
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Symmetric Weighted First-Order Model Counting
<span title="">2015</span>
<i title="ACM Press">
<a target="_blank" rel="noopener" href="https://fatcat.wiki/container/xtq6wnwaszaebg4qf7aw6mllwi" style="color: black;">Proceedings of the 34th ACM Symposium on Principles of Database Systems - PODS '15</a>
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For the combined complexity, we prove that, for every fragment FO k , k ≥ 2, the combined complexity of FOMC (or WFOMC) is #P-complete. 4 PTIME data complexity for symmetric WFOMC is called domain-liftability ...
It also does not characterize the tractability boundary: jtdb contains the γcyclic query above, but it does not contain the PTIME query c jtdb = R(x, y, z, u), S(x, y), T (x, z), V (x, u). ...
An open problem is to characterize the conjunctive queries without self-joins that are in polynomial time. ...
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The complexity of resilience and responsibility for self-join-free conjunctive queries
<span title="2015-11-01">2015</span>
<i title="VLDB Endowment">
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Further, we identify a mistake in a previous dichotomy for causal responsibility, and offer a revised characterization based purely on the structural form of the query (presence or absence of triads). ...
An explanation that is simple and concise is more likely to be correct and to provide an efficient resolution to a potential problem. ...
[29] defined a dichotomy for the view side-effect problem by providing a characterization that uses the query structure: DPview(q(y)) is PTIME for queries that are head dominated, and NP-complete otherwise ...
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Symmetric Weighted First-Order Model Counting
[article]
<span title="2015-06-01">2015</span>
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arXiv
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It also does not characterize the tractability boundary: jtdb contains the γcyclic query above, but it does not contain the PTIME query c jtdb = R(x, y, z, u), S(x, y), T (x, z), V (x, u). ...
An open problem is to characterize the conjunctive queries without self-joins that are in polynomial time. ...
PTIME DATA COMPLEXITY FOR FO 2 The proof of the fact that the data complexity for FO 2 is in PTIME is spread over two references, [35] and [37] . We include here a brief proof, for completeness. ...
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First order logic, fixed point logic and linear order
[chapter]
<span title="">1996</span>
<i title="Springer Berlin Heidelberg">
<a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a>
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LFP = PFP if and only if PTIME = PSPACE. ...
In order to state the complexity theoretic implications of a positive resolution of Conjecture 1, we i n troduce some notation. ...
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Semantic Complexity in Natural Language
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<span title="2015-08-21">2015</span>
<i title="John Wiley & Sons, Ltd">
The Handbook of Contemporary Semantic Theory
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We have NLogSpace ⊆ PTime ⊆ NPTime ⊆ ExpTime ⊆ NExpTime. Moreover, PTime is known to be a strict subset of ExpTime, and similarly for their non-deterministic counterparts. ...
Let o * be a new unary predicate. ...
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A syntactical analysis of non-size-increasing polynomial time computation
[article]
<span title="2001-09-14">2001</span>
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This leads to a nice characterization of Ptime. ...
Leivant and Marion [18] give a λ-calculus characterization of Ptime. ...
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