82,139 research outputs found

    Functional Dynamics I : Articulation Process

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    The articulation process of dynamical networks is studied with a functional map, a minimal model for the dynamic change of relationships through iteration. The model is a dynamical system of a function ff, not of variables, having a self-reference term f∘ff \circ f, introduced by recalling that operation in a biological system is often applied to itself, as is typically seen in rules in the natural language or genes. Starting from an inarticulate network, two types of fixed points are formed as an invariant structure with iterations. The function is folded with time, until it has finite or infinite piecewise-flat segments of fixed points, regarded as articulation. For an initial logistic map, attracted functions are classified into step, folded step, fractal, and random phases, according to the degree of folding. Oscillatory dynamics are also found, where function values are mapped to several fixed points periodically. The significance of our results to prototype categorization in language is discussed.Comment: 48 pages, 15 figeres (5 gif files

    Compiling ER Specifications into Declarative Programs

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    This paper proposes an environment to support high-level database programming in a declarative programming language. In order to ensure safe database updates, all access and update operations related to the database are generated from high-level descriptions in the entity- relationship (ER) model. We propose a representation of ER diagrams in the declarative language Curry so that they can be constructed by various tools and then translated into this representation. Furthermore, we have implemented a compiler from this representation into a Curry program that provides access and update operations based on a high-level API for database programming.Comment: Paper presented at the 17th Workshop on Logic-based Methods in Programming Environments (WLPE2007

    Digital implementation of the cellular sensor-computers

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    Two different kinds of cellular sensor-processor architectures are used nowadays in various applications. The first is the traditional sensor-processor architecture, where the sensor and the processor arrays are mapped into each other. The second is the foveal architecture, in which a small active fovea is navigating in a large sensor array. This second architecture is introduced and compared here. Both of these architectures can be implemented with analog and digital processor arrays. The efficiency of the different implementation types, depending on the used CMOS technology, is analyzed. It turned out, that the finer the technology is, the better to use digital implementation rather than analog

    Topological Semantics and Decidability

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    It is well-known that the basic modal logic of all topological spaces is S4S4. However, the structure of basic modal and hybrid logics of classes of spaces satisfying various separation axioms was until present unclear. We prove that modal logics of T0T_0, T1T_1 and T2T_2 topological spaces coincide and are S4.Wealsoexaminebasichybridlogicsoftheseclassesandprovetheirdecidability;aspartofthis,wefindoutthatthehybridlogicsof. We also examine basic hybrid logics of these classes and prove their decidability; as part of this, we find out that the hybrid logics of T_1andT2 and T_2 spaces coincide.Comment: presentation changes, results about concrete structure adde

    Invariant Synthesis for Incomplete Verification Engines

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    We propose a framework for synthesizing inductive invariants for incomplete verification engines, which soundly reduce logical problems in undecidable theories to decidable theories. Our framework is based on the counter-example guided inductive synthesis principle (CEGIS) and allows verification engines to communicate non-provability information to guide invariant synthesis. We show precisely how the verification engine can compute such non-provability information and how to build effective learning algorithms when invariants are expressed as Boolean combinations of a fixed set of predicates. Moreover, we evaluate our framework in two verification settings, one in which verification engines need to handle quantified formulas and one in which verification engines have to reason about heap properties expressed in an expressive but undecidable separation logic. Our experiments show that our invariant synthesis framework based on non-provability information can both effectively synthesize inductive invariants and adequately strengthen contracts across a large suite of programs
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