972 research outputs found

    Methods of class field theory to separate logics over finite residue classes and circuit complexity

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    This is a pre-copyedited, author-produced version of an article accepted for publication in Journal of logic and computation following peer review.Separations among the first-order logic Res(0,+,×) of finite residue classes, its extensions with generalized quantifiers, and in the presence of a built-in order are shown in this article, using algebraic methods from class field theory. These methods include classification of spectra of sentences over finite residue classes as systems of congruences, and the study of their h-densities over the set of all prime numbers, for various functions h on the natural numbers. Over ordered structures, the logic of finite residue classes and extensions are known to capture DLOGTIME-uniform circuit complexity classes ranging from AC to TC. Separating these circuit complexity classes is directly related to classifying the h-density of spectra of sentences in the corresponding logics of finite residue classes. General conditions are further shown in this work for a logic over the finite residue classes to have a sentence whose spectrum has no h-density. A corollary of this characterization of spectra of sentences is that in Res(0,+,×,<)+M, the logic of finite residue classes with built-in order and extended with the majority quantifier M, there are sentences whose spectrum have no exponential density.Peer ReviewedPostprint (author's final draft

    The 2nd Conference of PhD Students in Computer Science

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    Progress Report : 1991 - 1994

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    Non-equilibrium phase transitions in biomolecular signal transduction

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    We study a mechanism for reliable switching in biomolecular signal-transduction cascades. Steady bistable states are created by system-size cooperative effects in populations of proteins, in spite of the fact that the phosphorylation-state transitions of any molecule, by means of which the switch is implemented, are highly stochastic. The emergence of switching is a nonequilibrium phase transition in an energetically driven, dissipative system described by a master equation. We use operator and functional integral methods from reaction-diffusion theory to solve for the phase structure, noise spectrum, and escape trajectories and first-passage times of a class of minimal models of switches, showing how all critical properties for switch behavior can be computed within a unified framework

    Foundations of Software Science and Computation Structures

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    This open access book constitutes the proceedings of the 23rd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2020, which took place in Dublin, Ireland, in April 2020, and was held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The 31 regular papers presented in this volume were carefully reviewed and selected from 98 submissions. The papers cover topics such as categorical models and logics; language theory, automata, and games; modal, spatial, and temporal logics; type theory and proof theory; concurrency theory and process calculi; rewriting theory; semantics of programming languages; program analysis, correctness, transformation, and verification; logics of programming; software specification and refinement; models of concurrent, reactive, stochastic, distributed, hybrid, and mobile systems; emerging models of computation; logical aspects of computational complexity; models of software security; and logical foundations of data bases.
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