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Semantical characterizations and complexity of equivalences in answer set programming

Thomas Eiter, Michael Fink, Stefan Woltran
2007 ACM Transactions on Computational Logic  
complexity.  ...  For all these notions, we consider disjunctive logic programs in the propositional (ground) case as well as some restricted classes, providing semantical characterizations and analyzing the computational  ...  would like to thank David Pearce for interesting discussions and comments about this work and pointers to related literature, as well as Katsumi Inoue and Chiaki Sakama for their valuable remarks on relativizing  ... 
doi:10.1145/1243996.1244000 fatcat:m4on4rcfkjd7ff7emsd4koxsdq

Semantical Characterizations and Complexity of Equivalences in Answer Set Programming [article]

Thomas Eiter, Michael Fink, Stefan Woltran
2005 arXiv   pre-print
complexity.  ...  For all these notions, we consider disjunctive logic programs in the propositional (ground) case, as well as some restricted classes, provide semantical characterizations and analyze the computational  ...  would like to thank David Pearce for interesting discussions and comments about this work and pointers to related literature, as well as Katsumi Inoue and Chiaki Sakama for their valuable comments on relativizing  ... 
arXiv:cs/0502078v1 fatcat:7itqu6ujenatdozans3wz7zes4

Martin's Conjecture: A Classification of the Naturally Occurring Turing Degrees

Antonio Montalbán
2019 Notices of the American Mathematical Society  
Computability Theory Computability theory is the area of logic that studies the complexity of infinite countable objects.  ...  1 1 0 1 0 1 0 0 1 0 1 1 S Antonio Montalbán This paper is about naturally occurring objects in computability theory, the area inside mathematical logic that studies the complexity of infinite countable  ... 
doi:10.1090/noti1940 fatcat:gfm5r4rsezc5tda3y2myytt5su

Page 5097 of Mathematical Reviews Vol. , Issue 2000g [page]

2000 Mathematical Reviews  
which characterizes ACp as the non-uniformly first-order definable classes of finite structures.  ...  The significance of our investigation is conceptual, rather than technical: We identify ex- actly the logical analogue of uniform and non-uniform complexity classes.”  ... 

Page 7301 of Mathematical Reviews Vol. , Issue 97M [page]

1997 Mathematical Reviews  
Pnueli, Logics capturing relativized complexity classes uniformly (463-479); Eric Rosen and Scott Weinstein, Preservation theorems in finite model theory (480-502); Dan Suciu and Val Breazu-Tannen, A query  ...  {The papers will not be reviewed individually. } 97m:03005 03-06 03D15 68-06 68Q05 68Q15 % Workshop on Computability, Complexity and Logic.  ... 

Relativized depth [article]

Laurent Bienvenu, Valentino Delle Rose, Wolfgang Merkle
2021 arXiv   pre-print
oracles the relativized class is contained in the unrelativized class.  ...  Accordingly, for most notions for sets considered in computability theory, for the corresponding classes trivially for all oracles the unrelativized class is contained in the relativized class or for all  ...  This situation is captured quite well within the framework of depth.  ... 
arXiv:2112.04451v1 fatcat:e2mxyubyrrhz5pmwdflllewn34

Fixed-point logics, generalized quantifiers, and oracles

H Imhof
1997 Journal of Logic and Computation  
On ordered structures, where our results still hold, this reads as follows: For any given oracle Q, the complexity class PTIME Q (or PSPACE Q in a bounded oracle model) can be characterized by an extension  ...  However, there is no such logic L that satis es L(Q) PTIME Q (or PSPACE Q ) for all Q. We also study second order logic. Each level i of the polynomial hierarchy has a complete circuit problem.  ...  So, one could ask brie y: Is there a Lindstr om logic for oracle complexity classes?  ... 
doi:10.1093/logcom/7.3.405 fatcat:ti26eh7bzrczda33ejnlm3n3ju

Model-Theoretic Characterizations of Boolean and Arithmetic Circuit Classes of Small Depth [article]

Arnaud Durand, Anselm Haak, Heribert Vollmer
2017 arXiv   pre-print
In this paper we give a characterization of both Boolean and arithmetic circuit classes of logarithmic depth in the vein of descriptive complexity theory, i.e., the Boolean classes NC^1, SAC^1 and AC^1  ...  We build on Immerman's characterization of constant-depth polynomial-size circuits by formulas of first-order logic, i.e., AC^0 = FO, and augment the logical language with an operator for defining relations  ...  To further show the robustness of our classes, we want to mention certain variations of our logics that do not change the resulting complexity classes.  ... 
arXiv:1710.01934v2 fatcat:2haqhvlugzhv5mrzh3jp334y64

A Common View on Strong, Uniform, and Other Notions of Equivalence in Answer-Set Programming [article]

Stefan Woltran
2007 arXiv   pre-print
Moreover,we provide complexity bounds for the problem in question and sketch a possible implementation method. To appear in Theory and Practice of Logic Programming (TPLP).  ...  Logic programming under the answer-set semantics nowadays deals with numerous different notions of program equivalence.  ...  The class of all logic programs (over the fixed universe U) is denoted by C U .  ... 
arXiv:0712.0948v1 fatcat:kgshzsszgbe3fklcwwpdkyczki

Parameter free induction and provably total computable functions

Lev D. Beklemishev
1999 Theoretical Computer Science  
with the class of doubly recursive functions of Peter.  ...  These results are based on a precise characterization of ZC; and Zw in terms of reflection principles and conservation results for local reflection principles obtained by techniques of modal provability logic  ...  The above example of a natural pair of theories capturing the same class of computable functions, whose union captures a much bigger class, opens the question whether there may exist in general a unique  ... 
doi:10.1016/s0304-3975(98)00305-3 fatcat:an5vkane5beidkzgxwvziybb4q

Decidable Theories of the Ordering of Natural Numbers with Unary Predicates [chapter]

Alexander Rabinovich, Wolfgang Thomas
2006 Lecture Notes in Computer Science  
Expansions of the natural number ordering by unary predicates are studied, using logics which in expressive power are located between first-order and monadic second-order logic.  ...  a class of logics between first-order logic and monadic logic.  ...  There is a recursive uniformly homogeneous set for M with respect to the monadic (second-order) logic.  ... 
doi:10.1007/11874683_37 fatcat:3b443nbf65d7fer6qzxvxqhbvy

How to define a linear order on finite models

Lauri Hella, Phokion G. Kolaitis, Kerkko Luosto
1997 Annals of Pure and Applied Logic  
We carry out a systematic investigation of the definability of linear order on classes of finite rigid structures.  ...  PFP, infinitary logic Z!  ...  capturing the complexity class.  ... 
doi:10.1016/s0168-0072(97)00008-0 fatcat:5h4r4lawurdh5fknxdhrmxbafm

A common view on strong, uniform, and other notions of equivalence in answer-set programming

STEFAN WOLTRAN
2008 Theory and Practice of Logic Programming  
Moreover, we provide complexity bounds for the problem in question and sketch a possible implementation method making use of dedicated systems for checking ordinary equivalence.  ...  theoretical tools to compare incomplete programs and are defined by either restricting the syntactic structure of the considered context programsRor by bounding the set$\A$of atoms allowed to occur inR(relativized  ...  The class of all logic programs over universe U is denoted by C U .  ... 
doi:10.1017/s1471068407003250 fatcat:gaifw5b4cfgdncrrp7glsdexei

Equivalence between answer-set programs under (partially) fixed input

Bernhard Bliem, Stefan Woltran
2017 Annals of Mathematics and Artificial Intelligence  
We give full characterization results and a complexity analysis for the propositional case of rule equivalence and its relativized versions.  ...  Among the huge body of theoretical results, investigations of different equivalence notions between logic programs play a fundamental role for understanding modularity and optimization.  ...  to the class of unary programs.  ... 
doi:10.1007/s10472-017-9567-5 fatcat:qq2txtfykvg7li75euqt3wfppq

Discriminative Gaifman Models [article]

Mathias Niepert
2016 arXiv   pre-print
Considering local and bounded-size neighborhoods of knowledge bases renders logical inference and learning tractable, mitigates the problem of overfitting, and facilitates weight sharing.  ...  We can now state the following complexity result. d = (d 1 , ..., d n ), generated neighborhood N ∈ N r,k (d), and ϕ i ∈ Φ, we perform the substitution [s 1 /d 1 , ..., s n /d n ] and relativize ϕ i 's  ...  The expected probability of a representation of a neighborhood drawn uniformly at random from N (r,k) (d).  ... 
arXiv:1610.09369v1 fatcat:tvvlmhv27vf2zkzhjiwbqnqb3u
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