37,455 research outputs found
A Dual-Engine for Early Analysis of Critical Systems
This paper presents a framework for modeling, simulating, and checking
properties of critical systems based on the Alloy language -- a declarative,
first-order, relational logic with a built-in transitive closure operator. The
paper introduces a new dual-analysis engine that is capable of providing both
counterexamples and proofs. Counterexamples are found fully automatically using
an SMT solver, which provides a better support for numerical expressions than
the existing Alloy Analyzer. Proofs, however, cannot always be found
automatically since the Alloy language is undecidable. Our engine offers an
economical approach by first trying to prove properties using a
fully-automatic, SMT-based analysis, and switches to an interactive theorem
prover only if the first attempt fails. This paper also reports on applying our
framework to Microsoft's COM standard and the mark-and-sweep garbage collection
algorithm.Comment: Workshop on Dependable Software for Critical Infrastructures (DSCI),
Berlin 201
Bimodule structure of the mixed tensor product over and quantum walled Brauer algebra
We study a mixed tensor product of the three-dimensional fundamental
representations of the Hopf algebra , whenever is not a
root of unity. Formulas for the decomposition of tensor products of any simple
and projective -module with the generating modules
and are obtained. The centralizer of
on the chain is calculated. It is shown to be the quotient
of the quantum walled Brauer algebra. The structure of
projective modules over is written down explicitly. It is
known that the walled Brauer algebras form an infinite tower. We have
calculated the corresponding restriction functors on simple and projective
modules over . This result forms a crucial step in
decomposition of the mixed tensor product as a bimodule over
. We give an explicit bimodule
structure for all .Comment: 43 pages, 5 figure
Bimodule structure of the mixed tensor product over and quantum walled Brauer algebra
We study a mixed tensor product of the three-dimensional fundamental
representations of the Hopf algebra , whenever is not a
root of unity. Formulas for the decomposition of tensor products of any simple
and projective -module with the generating modules
and are obtained. The centralizer of
on the chain is calculated. It is shown to be the quotient
of the quantum walled Brauer algebra. The structure of
projective modules over is written down explicitly. It is
known that the walled Brauer algebras form an infinite tower. We have
calculated the corresponding restriction functors on simple and projective
modules over . This result forms a crucial step in
decomposition of the mixed tensor product as a bimodule over
. We give an explicit bimodule
structure for all .Comment: 43 pages, 5 figure
On absolute moments of characteristic polynomials of a certain class of complex random matrices
Integer moments of the spectral determinant of complex
random matrices are obtained in terms of the characteristic polynomial of
the Hermitian matrix for the class of matrices where is a
given matrix and is random unitary. This work is motivated by studies of
complex eigenvalues of random matrices and potential applications of the
obtained results in this context are discussed.Comment: 41 page, typos correcte
Deciding regular grammar logics with converse through first-order logic
We provide a simple translation of the satisfiability problem for regular
grammar logics with converse into GF2, which is the intersection of the guarded
fragment and the 2-variable fragment of first-order logic. This translation is
theoretically interesting because it translates modal logics with certain frame
conditions into first-order logic, without explicitly expressing the frame
conditions.
A consequence of the translation is that the general satisfiability problem
for regular grammar logics with converse is in EXPTIME. This extends a previous
result of the first author for grammar logics without converse. Using the same
method, we show how some other modal logics can be naturally translated into
GF2, including nominal tense logics and intuitionistic logic.
In our view, the results in this paper show that the natural first-order
fragment corresponding to regular grammar logics is simply GF2 without extra
machinery such as fixed point-operators.Comment: 34 page
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