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Approximate formulae for a logic that capture classes of computational complexity

A. Arratia, C. E. Ortiz
2008 Logic Journal of the IGPL  
This paper presents a syntax of approximate formulae suited for the logic with counting quantifiers SOLP.  ...  We introduce a concept of strong expressibility based on approximate formulae, and show that for many fragments of SOLP with built-in order, including ones that capture P and NL, expressibility and strong  ...  Acknowledgement The authors are grateful to the anonymous referee for his/her thoroughly revision of the original version of our paper, helping us improve it in form and contents.  ... 
doi:10.1093/jigpal/jzn031 fatcat:ynwytpkpqbhmtj7gb24l7ljbuy

On the Complexity of Model Expansion [chapter]

Antonina Kolokolova, Yongmei Liu, David Mitchell, Eugenia Ternovska
2010 Lecture Notes in Computer Science  
We study the complexity of model expansion (MX), which is the problem of expanding a given finite structure with additional relations to produce a finite model of a given formula.  ...  We present results on both data and combined complexity of MX for several fragments and extensions of FO that are relevant for this purpose, in particular the guarded fragment GF k of FO and extensions  ...  Acknowledgments The authors are grateful to the Natural Sciences and Engineering Council of Canada and to the Pacific Institute for Mathematical Sciences for financial support.  ... 
doi:10.1007/978-3-642-16242-8_32 fatcat:3rbwgsab3ba6fifzkw4v6d4vmq

Approximating the Expressive Power of Logics in Finite Models [chapter]

Argimiro Arratia, Carlos E. Ortiz
2004 Lecture Notes in Computer Science  
With this work we take steps towards understanding how well can we approximate, without a true order, the expressive power of logics that capture complexity classes on ordered structures.  ...  As of today, there is not known logical description of any computational complexity class below NP which does not requires a built-in linear order.  ...  TC 0 , since they coincide with known logics that capture these computational complexity classes, for example, first order logic extended with threshold quantifiers.  ... 
doi:10.1007/978-3-540-24698-5_57 fatcat:cpgtycksqzhutnyubrmc3gawly

The Complexity of Independence-Friendly Fixpoint Logic [chapter]

Julian Bradfield, Stephan Kreutzer
2005 Lecture Notes in Computer Science  
We study the complexity of model-checking for the fixpoint extension of Hintikka and Sandu's independence-friendly logic.  ...  We show that this logic captures ExpTime; and by embedding PFP, we show that its combined complexity is ExpSpace-hard, and moreover the logic includes second order logic (on finite structures).  ...  Acknowledgements Part of this work was done while the second author was a postdoctoral fellow in Edinburgh supported by the EU Research and Training Network GAMES (Games and Automata for Synthesis and  ... 
doi:10.1007/11538363_25 fatcat:n7ezlxjlknhbznyeqytnhlkw6m

Symmetric Computation (Invited Talk)

Anuj Dawar, Michael Wagner
2020 Annual Conference for Computer Science Logic  
This is at once a rich class of problems and one for which we have methods for proving lower bounds.  ...  For example, a widely used data model in the world of algorithm design is that of graphs, which captures a collection of entities and their pairwise relationships.  ...  Work in recent years has shown that FPC can be seen as capturing a natural class of symmetric algorithms inside P, with equivalent formulations in arising in circuit complexity and the theory of linear  ... 
doi:10.4230/lipics.csl.2020.2 dblp:conf/csl/Dawar20 fatcat:jdwa32g6rnfxhh5ed7mnjayrwe

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

Prabhu Manyem
2012 arXiv   pre-print
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.  ...  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).  ...  can be deduced that D requires a certain amount of resource (time and/or space) for its computation; that is, we can recognize the complexity class that D belongs to.  ... 
arXiv:1106.4606v5 fatcat:sttu6s2o2be6pd2y7yxazeknmu

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

2000 Mathematical Reviews  
While originally only DNF formulas were used as approximators, the symmetric version uses both CNF and DNF formulas.  ...  “Our first results are a slight generalization of similar results due to Molzan and can be stated as follows: Let C be one of L, NL, P, NP, PSpace and be a logic which captures C on ordered structures.  ... 

Page 2075 of Mathematical Reviews Vol. , Issue 2003C [page]

2003 Mathematical Reviews  
) A logic for approximate first-order reasoning.  ...  (E-MAL-AM; Malaga) ; Valverde, Agustin (E-MAL-AM; Malaga) Computing equilibrium models using signed formulas. (English summary) Computational logic—CL 2000 (London), 688-702, Lecture Notes in Comput.  ... 

Counting Proportions of Sets: Expressive Power with Almost Order [chapter]

Argimiro Arratia, Carlos E. Ortiz
2006 Lecture Notes in Computer Science  
fraction of elements in a subset of rtuples of a model that satisfy a formula.  ...  the fraction of elements in a subset of r-tuples of a model that satisfy a formula.  ...  is, for capturing the class P.  ... 
doi:10.1007/11682462_14 fatcat:eyo4z4oitfg6df3xbbchve53ve

Probabilistic verification and approximation

Richard Lassaigne, Sylvain Peyronnet
2008 Annals of Pure and Applied Logic  
Models of such systems are labelled discrete time Markov chains and checking specifications consists of computing satisfaction probabilities of linear temporal logic formulas.  ...  We prove that, in general, there is no polynomial time randomized approximation scheme with relative error for probabilistic verification.  ...  Acknowledgements We would like to thank Thomas Hérault for his important participation to the development of APMC, and an anonymous referee for his pertinent remarks and suggestions.  ... 
doi:10.1016/j.apal.2007.11.006 fatcat:kjhhgvh6prglxehlpepy42afju

Probabilistic Verification and Approximation

Richard Lassaigne, Sylvain Peyronnet
2006 Electronical Notes in Theoretical Computer Science  
Models of such systems are labelled discrete time Markov chains and checking specifications consists of computing satisfaction probabilities of linear temporal logic formulas.  ...  We prove that, in general, there is no polynomial time randomized approximation scheme with relative error for probabilistic verification.  ...  Acknowledgements We would like to thank Thomas Hérault for his important participation to the development of APMC, and an anonymous referee for his pertinent remarks and suggestions.  ... 
doi:10.1016/j.entcs.2005.05.031 fatcat:usjmmp4kjzdrnoztoxpskrguka

Coping with Incomplete Data: Recent Advances

Marco Console, Paolo Guagliardo, Leonid Libkin, Etienne Toussaint
2020 Proceedings of the 39th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems  
Work on the semantics of SQL was in conjunction with our collaboration with Neo4j Inc, supported by a grant from them.  ...  Finally, the third author is grateful to Foundation Sciences Mathématiques de Paris for supporting his stay in Paris in the Fall of 2019, during which some of this work was done.  ...  Hence computing it is a problem in a function class (rather than a complexity class capturing decision problems), and amounts to computing two numbers.  ... 
doi:10.1145/3375395.3387970 dblp:conf/pods/ConsoleGLT20 fatcat:j62xnjuxfbfx7bskzmf6hcg27a

On asymptotic probabilities in logics that capture DSPACE(log n) in presence of ordering [chapter]

Jerzy Tyszkiewicz
1993 Lecture Notes in Computer Science  
We show that for logics that capture DSPACE(log n) over ordered structures, and for recursive probability distributions on the class of nite models of the signature, the 0{1 law and the convergence law  ...  As one of the applications, we consider the conjecture of Kolaitis and Vardi, stating that for arbitrary probability distributions the 0{1 law holds for the logic L ! ! 1 !  ...  captures complexity class (see e.g. 5]), where the formulas Int; Eq; Succ and Edge were a priori chosen (to be atomic formulas) and xed.  ... 
doi:10.1007/3-540-56610-4_90 fatcat:bi6ktvxvnjdc3i4ln2mvryok6i

Logical Definability of Counting Functions

Kevin J. Compton, Erich Grädel
1996 Journal of computer and system sciences (Print)  
For a logic L, *L is the class of functions on finite structures counting the tuples (T , cÄ ) satisfying a given formula (T , cÄ ) in L.  ...  Saluja, Subrahmanyam, and Thakur showed that on classes of ordered structures *FO=*P (where FO denotes first-order logic) and that every function in * 1 has a fully polynomial randomized approximation  ...  A well studied complexity class of such functions is Valiant's class *P consisting of the functions that count the number of accepting computation paths of a given nondeterministic polynomial-time Turing  ... 
doi:10.1006/jcss.1996.0069 fatcat:fksc6h5r2jdg5nohcko3pxeawq

Other Complexity Classes and Measures [chapter]

Eric Allender, Michael Loui, Kenneth Regan
1998 Algorithms and Theory of Computation Handbook  
A common theme is that the new classes arise from the interaction of complexity theory with other fields, such as randomized algorithms, formal logic, combinatorial optimization, and matrix algebra.  ...  Probabilistic Complexity Classes Since the 1970s, with the development of randomized algorithms for computational problems (see Chapter 15), complexity theorists have placed randomized algorithms on a  ...  Just as machines of a particular type define complexity classes, so also do logical formulas of a particular type define important classes of languages.  ... 
doi:10.1201/9781420049503-c30 fatcat:gwoukqhjy5gsjlwxfoxcdojwzm
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