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

Thomas A. Henzinger
1998 Lecture Notes in Computer Science  
Our main focus 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  ... 
doi:10.1007/bfb0055640 fatcat:bo67724m4nf5rgevaqp6ejhvcu

Is Polynomial Time Choiceless? [chapter]

Erich Grädel, Martin Grohe
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?  ... 
doi:10.1007/978-3-319-23534-9_11 fatcat:n6rczztse5g4nezyzahgrmis3q

Choiceless polynomial time

Andreas Blass, Yuri Gurevich, Saharon Shelah
1999 Annals of Pure and Applied Logic  
This question can be recast as follows: Does 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.  ... 
doi:10.1016/s0168-0072(99)00005-6 fatcat:gqnccerwmfd5pdyvg6k33q72ue

Efficient timed model checking for discrete-time systems

F. Laroussinie, N. Markey, Ph. Schnoebelen
2006 Theoretical Computer Science  
Two semantics 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.  ... 
doi:10.1016/j.tcs.2005.11.020 fatcat:azwf654hljcmtmvouvbv6xgucq

Elementary Linear Logic Revisited for Polynomial Time and an Exponential Time Hierarchy [chapter]

Patrick Baillot
2011 Lecture Notes in Computer Science  
We characterize in this way the class P of 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.  ... 
doi:10.1007/978-3-642-25318-8_25 fatcat:bomvp25otnfxhnr7ck7udoaxda

Soft linear logic and polynomial time

Y LAFONT
2004 Theoretical Computer Science  
We present 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.  ... 
doi:10.1016/s0304-3975(03)00523-1 fatcat:hm25sv3cjfbnhe6kn6jhw3uuru

Soft linear logic and polynomial time

Yves Lafont
2004 Theoretical Computer Science  
We present 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.  ... 
doi:10.1016/j.tcs.2003.10.018 fatcat:xrh6il4cm5duphutvoxjcg6kni

Choiceless polynomial time [article]

Andreas Blass, Yuri Gurevich, Saharon Shelah
1997 arXiv   pre-print
This question can be recast as follows: Does 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.  ... 
arXiv:math/9705225v1 fatcat:5i3bafda25ezvnjyqwxd47e2uy

Insignificant Choice Polynomial Time [article]

Klaus-Dieter Schewe
2021 arXiv   pre-print
In the late 1980s Gurevich conjectured that 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.  ... 
arXiv:2005.04598v7 fatcat:6zvwqgmmwvgwfcfqfhrhdvplou

Time, Hardware, and Uniformity [chapter]

David Mix Barrington, Neil Immerman
1997 Complexity Theory Retrospective II  
We describe three orthogonal complexity measures: parallel 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.  ... 
doi:10.1007/978-1-4612-1872-2_1 fatcat:sbpijo2dojhyvbwokdmjazlnue

Syntactic Characterisations of Polynomial-Time Optimisation Classes (Syntactic Characterizations of Polynomial-Time Optimization Classes) [article]

Prabhu Manyem
2006 arXiv   pre-print
In Descriptive Complexity, 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.  ... 
arXiv:cs/0606050v2 fatcat:rkgflaaqqnadbj2p2x6rmmappm

Polymorphic recursion and subtype qualifications: Polymorphic binding-time analysis in polynomial time [chapter]

Dirk Dussart, Fritz Henglein, Christian Mossin
1995 Lecture Notes in Computer Science  
The punch-line of the development 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.  ... 
doi:10.1007/3-540-60360-3_36 fatcat:pjeutkttwfbabclrqas4rgxii4

Solving 3-SAT and 3-dimensional matching in polynomial time [article]

Frederic Gillet
2014 arXiv   pre-print
We show how the implementation of conservative 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  ... 
arXiv:1310.1971v6 fatcat:jkyunxe4dzhixjybs3njl35454

A Fragment of Dependence Logic Capturing Polynomial Time

Johannes Ebbing, Juha Kontinen, Julian-Steffen Müller, Heribert Vollmer, Erich Grädel
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 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.  ... 
doi:10.2168/lmcs-10(3:3)2014 fatcat:pyyls2nzn5bkhpbhjfvycfxxla

Bernstein's socks and polynomial-time provable coherence [article]

Alessio Benavoli and Alessandro Facchini and Marco Zaffalon
2019 arXiv   pre-print
It 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).  ... 
arXiv:1903.04406v1 fatcat:c7wgx25j2nhili4li6scbpsmeq
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