37,455 research outputs found

    A Dual-Engine for Early Analysis of Critical Systems

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    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 Uqs(21)U_{q} s\ell(2|1) and quantum walled Brauer algebra

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    We study a mixed tensor product 3m3n\mathbf{3}^{\otimes m} \otimes \mathbf{\overline{3}}^{\otimes n} of the three-dimensional fundamental representations of the Hopf algebra Uqs(21)U_{q} s\ell(2|1), whenever qq is not a root of unity. Formulas for the decomposition of tensor products of any simple and projective Uqs(21)U_{q} s\ell(2|1)-module with the generating modules 3\mathbf{3} and 3\mathbf{\overline{3}} are obtained. The centralizer of Uqs(21)U_{q} s\ell(2|1) on the chain is calculated. It is shown to be the quotient Xm,n\mathscr{X}_{m,n} of the quantum walled Brauer algebra. The structure of projective modules over Xm,n\mathscr{X}_{m,n} 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 Xm,n\mathscr{X}_{m,n}. This result forms a crucial step in decomposition of the mixed tensor product as a bimodule over Xm,nUqs(21)\mathscr{X}_{m,n}\boxtimes U_{q} s\ell(2|1). We give an explicit bimodule structure for all m,nm,n.Comment: 43 pages, 5 figure

    Bimodule structure of the mixed tensor product over Uqs(21)U_{q} s\ell(2|1) and quantum walled Brauer algebra

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    We study a mixed tensor product 3m3n\mathbf{3}^{\otimes m} \otimes \mathbf{\overline{3}}^{\otimes n} of the three-dimensional fundamental representations of the Hopf algebra Uqs(21)U_{q} s\ell(2|1), whenever qq is not a root of unity. Formulas for the decomposition of tensor products of any simple and projective Uqs(21)U_{q} s\ell(2|1)-module with the generating modules 3\mathbf{3} and 3\mathbf{\overline{3}} are obtained. The centralizer of Uqs(21)U_{q} s\ell(2|1) on the chain is calculated. It is shown to be the quotient Xm,n\mathscr{X}_{m,n} of the quantum walled Brauer algebra. The structure of projective modules over Xm,n\mathscr{X}_{m,n} 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 Xm,n\mathscr{X}_{m,n}. This result forms a crucial step in decomposition of the mixed tensor product as a bimodule over Xm,nUqs(21)\mathscr{X}_{m,n}\boxtimes U_{q} s\ell(2|1). We give an explicit bimodule structure for all m,nm,n.Comment: 43 pages, 5 figure

    On absolute moments of characteristic polynomials of a certain class of complex random matrices

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    Integer moments of the spectral determinant det(zIW)2|\det(zI-W)|^2 of complex random matrices WW are obtained in terms of the characteristic polynomial of the Hermitian matrix WWWW^* for the class of matrices W=AUW=AU where AA is a given matrix and UU 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

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    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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