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It's about time: Real-time logics reviewed
[chapter]

1998
*
Lecture Notes in Computer Science
*

Our main focus

doi:10.1007/bfb0055640
fatcat:bo67724m4nf5rgevaqp6ejhvcu
*is*on tableau constructions*for*model checking linear temporal formulas with*timing*constraints. ... In particular, we nd that*a*great deal of real-*time*veri cation can be performed in*polynomial*space, but also that considerable care must be exercised in order to keep the real-*time*veri cation problem ... The author thanks Jean-Francois Raskin*for*several valuable suggestions on*a*draft of this paper, Prasad Sistla*for*repeatedly pointing out the importance of*polynomial*-space fragments of real-*time**logics*...##
###
Is Polynomial Time Choiceless?
[chapter]

2015
*
Lecture Notes in Computer Science
*

*A*long

*time*ago, Yuri Gurevich made precise the problem of whether

*there*

*is*

*a*

*logic*capturing

*polynomial*-

*time*on arbitrary finite structures, and conjectured that no such

*logic*exists. ... Nevertheless, together with Andreas Blass and Saharon Shelah, he has also proposed what still seems to be the most promising candidate

*for*

*a*

*logic*

*for*

*polynomial*

*time*, namely Choiceless

*Polynomial*

*Time*... Introduction

*Is*

*there*

*a*

*logic*

*for*Ptime? ...

##
###
Choiceless polynomial time

1999
*
Annals of Pure and Applied Logic
*

This question can be recast as follows: Does

doi:10.1016/s0168-0072(99)00005-6
fatcat:gqnccerwmfd5pdyvg6k33q72ue
*there*exist*a**logic*that captures*polynomial**time*(without presuming the presence of*a*linear order)? Earlier, one of us conjectured*a*negative answer. ... Turing machines deÿne*polynomial**time*(PTime) on strings but cannot deal with structures like graphs directly, and*there**is*no known, easily computable string encoding of isomorphism classes of structures ... Bipartite Matching*is*not inCPTime + . Proof. We can use exactly the same proof as*for*Theorem 43, because the two structures used in that proof had the same cardinality. ...##
###
Efficient timed model checking for discrete-time systems

2006
*
Theoretical Computer Science
*

Two semantics

doi:10.1016/j.tcs.2005.11.020
fatcat:azwf654hljcmtmvouvbv6xgucq
*for*DTGs are presented and motivated. We consider*timed*versions of CTL where subscripts put quantitative constraints on the*time*it takes before*a*property*is*satisfied. ... Without exact durations, model checking can be done in*polynomial**time*, but with exact durations, it becomes p 2 -complete or PSPACE-complete depending on the considered semantics. ... Acknowledgments We thank Jeremy Sproston*for*discussing the proof of Theorem 5.3 with us, and the anonymous referees*for*their useful remarks. ...##
###
Elementary Linear Logic Revisited for Polynomial Time and an Exponential Time Hierarchy
[chapter]

2011
*
Lecture Notes in Computer Science
*

We characterize in this way the class P of

doi:10.1007/978-3-642-25318-8_25
fatcat:bomvp25otnfxhnr7ck7udoaxda
*polynomial**time*predicates and more generally the hierarchy of classes k-EXP,*for*k ≥ 0, where k-EXP*is*the union of DTIME(2 n i k ),*for*i ≥ 1. ... Elementary linear*logic**is**a*simple variant of linear*logic*, introduced by Girard and which characterizes in the proofs-as-programs approach the class of elementary functions (computable in*time*bounded ... The author would like to thank Jean-Yves Girard whose initial question, whether P could be characterized in elementary linear*logic*, triggered this work. ...##
###
Soft linear logic and polynomial time

2004
*
Theoretical Computer Science
*

We present

doi:10.1016/s0304-3975(03)00523-1
fatcat:hm25sv3cjfbnhe6kn6jhw3uuru
*a*subsystem of second-order linear*logic*with restricted rules*for*exponentials so that proofs correspond to*polynomial**time*algorithms, and vice versa. ... If*a*predicate on boolean strings*is*computable by*a*Turing machine in*polynomial**time*P(n) and in*polynomial*space Q(n),*there**is**a*generic proof*for*the sequent S (deg P+deg Q+1) B which corresponds ... Soft linear*logic*can be seen as*a*subsystem of bounded linear*logic*which*is*powerful enough to encode*polynomial**time*. It*is*simpler than bounded linear*logic*and light linear*logic*. ...##
###
Soft linear logic and polynomial time

2004
*
Theoretical Computer Science
*

We present

doi:10.1016/j.tcs.2003.10.018
fatcat:xrh6il4cm5duphutvoxjcg6kni
*a*subsystem of second-order linear*logic*with restricted rules*for*exponentials so that proofs correspond to*polynomial**time*algorithms, and vice versa. ... If*a*predicate on boolean strings*is*computable by*a*Turing machine in*polynomial**time*P(n) and in*polynomial*space Q(n),*there**is**a*generic proof*for*the sequent S (deg P+deg Q+1) B which corresponds ... Soft linear*logic*can be seen as*a*subsystem of bounded linear*logic*which*is*powerful enough to encode*polynomial**time*. It*is*simpler than bounded linear*logic*and light linear*logic*. ...##
###
Choiceless polynomial time
[article]

1997
*
arXiv
*
pre-print

This question can be recast as follows: Does

arXiv:math/9705225v1
fatcat:5i3bafda25ezvnjyqwxd47e2uy
*there*exist*a**logic*that captures*polynomial**time*(without presuming the presence of*a*linear order)? Earlier, one of us conjectured the negative answer. ... Turing machines define*polynomial**time*(PTime) on strings but cannot deal with structures like graphs directly, and*there**is*no known, easily computable string encoding of isomorphism classes of structures ...*A*language X*is*PTime if*there*exists*a*PTime Turing machine (that*is**polynomial**time*bounded Turing machine) that accepts exactly the strings in X. ...##
###
Insignificant Choice Polynomial Time
[article]

2021
*
arXiv
*
pre-print

In the late 1980s Gurevich conjectured that

arXiv:2005.04598v7
fatcat:6zvwqgmmwvgwfcfqfhrhdvplou
*there**is*no*logic*capturing PTIME, where*logic*has to be understood in*a*very general way comprising computation models over structures. ... Such*a*version of*polynomially*bounded ASMs, which we call insignificant choice*polynomial**time*(ICPT) will indeed capture PTIME. ... Acknowledgements I am grateful to Egon Börger and Flavio Ferrarotti*for*carefully reading my manuscript and making many suggestions*for*improvement. ...##
###
Time, Hardware, and Uniformity
[chapter]

1997
*
Complexity Theory Retrospective II
*

We describe three orthogonal complexity measures: parallel

doi:10.1007/978-1-4612-1872-2_1
fatcat:sbpijo2dojhyvbwokdmjazlnue
*time*, amount of hardware, and degree of non-uniformity, which together parametrize most complexity classes. ...*A*fairly simple picture arises in which the basic questions in complexity theory | solved and unsolved | can be understood as questions about tradeo s among these three dimensions. ... Thanks also to Chi-Jen Lu, Ken Regan, and Zhi-Li Zhang*for*valuable discussions. ...##
###
Syntactic Characterisations of Polynomial-Time Optimisation Classes (Syntactic Characterizations of Polynomial-Time Optimization Classes)
[article]

2006
*
arXiv
*
pre-print

In Descriptive Complexity,

arXiv:cs/0606050v2
fatcat:rkgflaaqqnadbj2p2x6rmmappm
*there**is**a*vast amount of literature on decision problems, and their classes such as P, NP, L and NL. ... Grädel characterised the*polynomial*class P of decision problems. ... Radhakrishnan and*A*. Panconesi at TIFR (Mumbai).*A*preliminary version of the paper was presented at the Algorithms and Complexity in Durham (ACiD 2005) workshop at Durham, UK. ...##
###
Polymorphic recursion and subtype qualifications: Polymorphic binding-time analysis in polynomial time
[chapter]

1995
*
Lecture Notes in Computer Science
*

The punch-line of the development

doi:10.1007/3-540-60360-3_36
fatcat:pjeutkttwfbabclrqas4rgxii4
*is*that*a*very simple modification of the basic algorithm reduces its computational complexity from exponential*time*to*polynomial**time*relative to the size of the given ... This solves the open problem of finding an inference algorithm*for*polymorphic binding-*time*analysis [7] . ... It can be checked to see that*there*goes no more than*time**polynomial*in m in between two clicks. ...##
###
Solving 3-SAT and 3-dimensional matching in polynomial time
[article]

2014
*
arXiv
*
pre-print

We show how the implementation of conservative

arXiv:1310.1971v6
fatcat:jkyunxe4dzhixjybs3njl35454
*logic*gates on flow networks suggests*a*way to solve 3SAT and 3-dimensional matching problems in*polynomial**time*by using standard minimum-cost flow methods ... But*a*valid solution can be found very efficiently (in*polynomial**time*) by transforming the problem into*a*maximum flow problem. ... Several algorithms exist that can solve minimum cost flows efficiently (*polynomial*both in*time*and in space), like the "minimum-mean cycle-canceling" algorithm [ref 1, 2] . 2) Conservative*logical*...##
###
A Fragment of Dependence Logic Capturing Polynomial Time

2014
*
Logical Methods in Computer Science
*

Therefore we define an even smaller fragment D-Horn* and show that over finite successor structures it captures the complexity class P of all sets decidable in

doi:10.2168/lmcs-10(3:3)2014
fatcat:pyyls2nzn5bkhpbhjfvycfxxla
*polynomial**time*. ... Furthermore we study the question which of our results can ge generalized to the case of open formulae of D-Horn* and so-called downwards monotone*polynomial**time*properties of teams. ... We say that*a*class D of structures*is*downwards closed with respect to R if*for*every structure*A*the following holds: if*A*∈ D and Q ⊆ R*A*then*A*′ ∈ D, where*A*′ arises from*A*by replacing R*A*by Q. ...##
###
Bernstein's socks and polynomial-time provable coherence
[article]

2019
*
arXiv
*
pre-print

It

arXiv:1903.04406v1
fatcat:c7wgx25j2nhili4li6scbpsmeq
*is*based on the unique requirement that being non-negative*for**a*gamble has to be defined so that it can be provable in*polynomial*-*time*. ... We recently introduced*a*bounded rationality approach*for*the theory of desirable gambles. ... (irrationality) to represent anything else than*a*situation of incoherence (irrationality), and thus*for*which, seen as*a*theory of*a**logic*,*there**is*no "natural" model (in the dual space). ...
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