135,109 research outputs found

    Formalization of Universal Algebra in Agda

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    In this work we present a novel formalization of universal algebra in Agda. We show that heterogeneous signatures can be elegantly modelled in type-theory using sets indexed by arities to represent operations. We prove elementary results of heterogeneous algebras, including the proof that the term algebra is initial and the proofs of the three isomorphism theorems. We further formalize equational theory and prove soundness and completeness. At the end, we define (derived) signature morphisms, from which we get the contravariant functor between algebras; moreover, we also proved that, under some restrictions, the translation of a theory induces a contra-variant functor between models.Fil: Gunther, Emmanuel. Universidad Nacional de CĂłrdoba. Facultad de MatemĂĄtica, AstronomĂ­a y FĂ­sica; Argentina. Consejo Nacional de Investigaciones CientĂ­ficas y TĂ©cnicas; ArgentinaFil: Gadea, Alejandro Emilio. Universidad Nacional de CĂłrdoba. Facultad de MatemĂĄtica, AstronomĂ­a y FĂ­sica; Argentina. Consejo Nacional de Investigaciones CientĂ­ficas y TĂ©cnicas; ArgentinaFil: Pagano, Miguel Maria. Consejo Nacional de Investigaciones CientĂ­ficas y TĂ©cnicas; Argentina. Universidad Nacional de CĂłrdoba. Facultad de MatemĂĄtica, AstronomĂ­a y FĂ­sica; Argentin

    A Survey on Continuous Time Computations

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    We provide an overview of theories of continuous time computation. These theories allow us to understand both the hardness of questions related to continuous time dynamical systems and the computational power of continuous time analog models. We survey the existing models, summarizing results, and point to relevant references in the literature

    On computing fixpoints in well-structured regular model checking, with applications to lossy channel systems

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    We prove a general finite convergence theorem for "upward-guarded" fixpoint expressions over a well-quasi-ordered set. This has immediate applications in regular model checking of well-structured systems, where a main issue is the eventual convergence of fixpoint computations. In particular, we are able to directly obtain several new decidability results on lossy channel systems.Comment: 16 page

    Multistage Voting Model with Alternative Elimination

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    The voting process is formalized as a multistage voting model with successive alternative elimination. A finite number of agents vote for one of the alternatives each round subject to their preferences. If the number of votes given to the alternative is less than a threshold, it gets eliminated from the game. A special subclass of repeated games that always stop after a finite number of stages is considered. Threshold updating rule is proposed. A computer simulation is used to illustrate two properties of these voting games

    Legal Information and the Development of American Law: Writings on the Form and Structure of the Published Law

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    Robert C. Berring\u27s writings about the impacts of electronic databases, the Internet, and other communications technologies on legal research and practice are an essential part of a larger literature that explores the ways in which the forms and structures of published legal information have influenced how American lawyers think about the law. This paper reviews Berring\u27s writings, along with those of other writers concerned with these questions, focusing on the implications of Berring\u27s idea that in the late nineteenth century American legal publishers created a conceptual universe of thinkable thoughts through which U.S. lawyers came to view the law. It concludes that, spurred by Berring and others, the literature of legal information has become far reaching in scope and interdisciplinary in approach, while the themes struck in Berring\u27s work continue to inform the scholarship of newer writers
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