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Approximate formulae for a logic that capture classes of computational complexity

2008
*
Logic Journal of the IGPL
*

This paper presents

doi:10.1093/jigpal/jzn031
fatcat:ynwytpkpqbhmtj7gb24l7ljbuy
*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. ...##
###
On the Complexity of Model Expansion
[chapter]

2010
*
Lecture Notes in Computer Science
*

We study the

doi:10.1007/978-3-642-16242-8_32
fatcat:3rbwgsab3ba6fifzkw4v6d4vmq
*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. ...##
###
Approximating the Expressive Power of Logics in Finite Models
[chapter]

2004
*
Lecture Notes in Computer Science
*

With this work we take steps towards understanding how well can we

doi:10.1007/978-3-540-24698-5_57
fatcat:cpgtycksqzhutnyubrmc3gawly
*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. ...##
###
The Complexity of Independence-Friendly Fixpoint Logic
[chapter]

2005
*
Lecture Notes in Computer Science
*

We study the

doi:10.1007/11538363_25
fatcat:n7ezlxjlknhbznyeqytnhlkw6m
*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 ...##
###
Symmetric Computation (Invited Talk)

2020
*
Annual Conference for Computer Science Logic
*

This is at once

doi:10.4230/lipics.csl.2020.2
dblp:conf/csl/Dawar20
fatcat:jdwa32g6rnfxhh5ed7mnjayrwe
*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 ...##
###
Expressibility at the machine level versus structure level: ESO universal Horn Logic and the class P
[article]

2012
*
arXiv
*
pre-print

We show

arXiv:1106.4606v5
fatcat:sttu6s2o2be6pd2y7yxazeknmu
*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. ...##
###
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]

2006
*
Lecture Notes in Computer Science
*

fraction

doi:10.1007/11682462_14
fatcat:eyo4z4oitfg6df3xbbchve53ve
*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. ...##
###
Probabilistic verification and approximation

2008
*
Annals of Pure and Applied Logic
*

Models

doi:10.1016/j.apal.2007.11.006
fatcat:kjhhgvh6prglxehlpepy42afju
*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. ...##
###
Probabilistic Verification and Approximation

2006
*
Electronical Notes in Theoretical Computer Science
*

Models

doi:10.1016/j.entcs.2005.05.031
fatcat:usjmmp4kjzdrnoztoxpskrguka
*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. ...##
###
Coping with Incomplete Data: Recent Advances

2020
*
Proceedings of the 39th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems
*

Work on the semantics

doi:10.1145/3375395.3387970
dblp:conf/pods/ConsoleGLT20
fatcat:j62xnjuxfbfx7bskzmf6hcg27a
*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. ...##
###
On asymptotic probabilities in logics that capture DSPACE(log n) in presence of ordering
[chapter]

1993
*
Lecture Notes in Computer Science
*

We show

doi:10.1007/3-540-56610-4_90
fatcat:bi6ktvxvnjdc3i4ln2mvryok6i
*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. ...##
###
Logical Definability of Counting Functions

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 ...

##
###
Other Complexity Classes and Measures
[chapter]

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. ...

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