6,483 research outputs found
Two-Variable Logic with Two Order Relations
It is shown that the finite satisfiability problem for two-variable logic
over structures with one total preorder relation, its induced successor
relation, one linear order relation and some further unary relations is
EXPSPACE-complete. Actually, EXPSPACE-completeness already holds for structures
that do not include the induced successor relation. As a special case, the
EXPSPACE upper bound applies to two-variable logic over structures with two
linear orders. A further consequence is that satisfiability of two-variable
logic over data words with a linear order on positions and a linear order and
successor relation on the data is decidable in EXPSPACE. As a complementing
result, it is shown that over structures with two total preorder relations as
well as over structures with one total preorder and two linear order relations,
the finite satisfiability problem for two-variable logic is undecidable
Robustness of a bisimulation-type faster-than preorder
TACS is an extension of CCS where upper time bounds for delays can be
specified. Luettgen and Vogler defined three variants of bismulation-type
faster-than relations and showed that they all three lead to the same preorder,
demonstrating the robustness of their approach. In the present paper, the
operational semantics of TACS is extended; it is shown that two of the variants
still give the same preorder as before, underlining robustness. An explanation
is given why this result fails for the third variant. It is also shown that
another variant, which mixes old and new operational semantics, can lead to
smaller relations that prove the same preorder.Comment: Express Worksho
Spectral preorder and perturbations of discrete weighted graphs
In this article, we introduce a geometric and a spectral preorder relation on
the class of weighted graphs with a magnetic potential. The first preorder is
expressed through the existence of a graph homomorphism respecting the magnetic
potential and fulfilling certain inequalities for the weights. The second
preorder refers to the spectrum of the associated Laplacian of the magnetic
weighted graph. These relations give a quantitative control of the effect of
elementary and composite perturbations of the graph (deleting edges,
contracting vertices, etc.) on the spectrum of the corresponding Laplacians,
generalising interlacing of eigenvalues.
We give several applications of the preorders: we show how to classify graphs
according to these preorders and we prove the stability of certain eigenvalues
in graphs with a maximal d-clique. Moreover, we show the monotonicity of the
eigenvalues when passing to spanning subgraphs and the monotonicity of magnetic
Cheeger constants with respect to the geometric preorder. Finally, we prove a
refined procedure to detect spectral gaps in the spectrum of an infinite
covering graph.Comment: 26 pages; 8 figure
Logical Characterizations of Behavioral Relations on Transition Systems of Probability Distributions
Probabilistic nondeterministic processes are commonly modeled as probabilistic LTSs (PLTSs). A number of logical characterizations of the main behavioral relations on PLTSs have been studied. In particular, Parma and Segala [2007] and Hermanns et al. [2011] define a probabilistic Hennessy-Milner logic interpreted over probability distributions, whose corresponding logical equivalence/preorder when restricted to Dirac distributions coincide with standard bisimulation/simulation between the states of a PLTS. This result is here extended by studying the full logical equivalence/preorder between (possibly non-Dirac) distributions in terms of a notion of bisimulation/simulation defined on a LTS whose states are distributions (dLTS). We show that the well-known spectrum of behavioral relations on nonprobabilistic LTSs as well as their corresponding logical characterizations in terms of Hennessy-Milner logic scales to the probabilistic setting when considering dLTSs
Conformance Testing with Labelled Transition Systems: Implementation Relations and Test Generation
This paper studies testing based on labelled transition systems, presenting two test generation algorithms with their corresponding implementation relations. The first algorithm assumes that implementations communicate with their environment via symmetric, synchronous interactions. It is based on the theory of testing equivalence and preorder, as is most of the testing theory for labelled transition systems, and it is found in the literature in some slightly different variations. The second algorithm is based on the assumption that implementations communicate with their environment via inputs and outputs. Such implementations are formalized by restricting the class of labelled transition systems to those systems that can always accept input actions. For these implementations a testing theory is developed, analogous to the theory of testing equivalence and preorder. It consists of implementation relations formalizing the notion of conformance of these implementations with respect to labelled transition system specifications, test cases and test suites, test execution, the notion of passing a test suite, and the test generation algorithm, which is proved to produce sound test suites for one of the implementation relations
Fuzzy Galois connections on fuzzy sets
In fairly elementary terms this paper presents how the theory of preordered
fuzzy sets, more precisely quantale-valued preorders on quantale-valued fuzzy
sets, is established under the guidance of enriched category theory. Motivated
by several key results from the theory of quantaloid-enriched categories, this
paper develops all needed ingredients purely in order-theoretic languages for
the readership of fuzzy set theorists, with particular attention paid to fuzzy
Galois connections between preordered fuzzy sets.Comment: 30 pages, final versio
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