87 research outputs found
Expressiveness and complexity of graph logic
We investigate the complexity and expressive power of the spatial logic for querying graphs introduced by Cardelli, Gardner and Ghelli (ICALP 2002).We show that the model-checking complexity of versions of this logic with and without recursion is PSPACE-complete. In terms of expressive power, the version without recursion is a fragment of the monadic second-order logic of graphs and we show that it can express complete problems at every level of the polynomial hierarchy. We also show that it can define all regular languages, when interpretation is restricted to strings. The expressive power of the logic with recursion is much greater as it can express properties that are PSPACE-complete and therefore unlikely to be definable in second-order logic
A Logic that Captures P on Ordered Structures
We extend the inflationary fixed-point logic, IFP, with a new kind of
second-order quantifiers which have (poly-)logarithmic bounds. We prove that on
ordered structures the new logic captures
the limited nondeterminism class . In order to study its
expressive power, we also design a new version of Ehrenfeucht-Fra\"iss\'e game
for this logic and show that our capturing result will not hold on the general
case, i.e. on all the finite structures.Comment: 15 pages. This article was reported with a title "Logarithmic-Bounded
Second-Order Quantifiers and Limited Nondeterminism" in National Conference
on Modern Logic 2019, on November 9 in Beijin
On two-variable guarded fragment logic with expressive local Presburger constraints
We consider the extension of two-variable guarded fragment logic with local
Presburger quantifiers. These are quantifiers that can express properties such
as ``the number of incoming blue edges plus twice the number of outgoing red
edges is at most three times the number of incoming green edges'' and captures
various description logics with counting, but without constant symbols. We show
that the satisfiability of this logic is EXP-complete. While the lower bound
already holds for the standard two-variable guarded fragment logic, the upper
bound is established by a novel, yet simple deterministic graph theoretic based
algorithm
Distributed Graph Automata and Verification of Distributed Algorithms
Combining ideas from distributed algorithms and alternating automata, we
introduce a new class of finite graph automata that recognize precisely the
languages of finite graphs definable in monadic second-order logic. By
restricting transitions to be nondeterministic or deterministic, we also obtain
two strictly weaker variants of our automata for which the emptiness problem is
decidable. As an application, we suggest how suitable graph automata might be
useful in formal verification of distributed algorithms, using Floyd-Hoare
logic.Comment: 26 pages, 6 figures, includes a condensed version of the author's
Master's thesis arXiv:1404.6503. (This version of the article (v2) is
identical to the previous one (v1), except for minor changes in phrasing.
Descriptive complexity for pictures languages (extended abstract)
This paper deals with descriptive complexity of picture languages of any
dimension by syntactical fragments of existential second-order logic.
- We uniformly generalize to any dimension the characterization by
Giammarresi et al. \cite{GRST96} of the class of \emph{recognizable} picture
languages in existential monadic second-order logic. - We state several logical
characterizations of the class of picture languages recognized in linear time
on nondeterministic cellular automata of any dimension. They are the first
machine-independent characterizations of complexity classes of cellular
automata.
Our characterizations are essentially deduced from normalization results we
prove for first-order and existential second-order logics over pictures. They
are obtained in a general and uniform framework that allows to extend them to
other "regular" structures. Finally, we describe some hierarchy results that
show the optimality of our logical characterizations and delineate their
limits.Comment: 33 pages - Submited to Lics 201
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