244 research outputs found

    Completeness and Incompleteness of Synchronous Kleene Algebra

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    Synchronous Kleene algebra (SKA), an extension of Kleene algebra (KA), was proposed by Prisacariu as a tool for reasoning about programs that may execute synchronously, i.e., in lock-step. We provide a countermodel witnessing that the axioms of SKA are incomplete w.r.t. its language semantics, by exploiting a lack of interaction between the synchronous product operator and the Kleene star. We then propose an alternative set of axioms for SKA, based on Salomaa's axiomatisation of regular languages, and show that these provide a sound and complete characterisation w.r.t. the original language semantics.Comment: Accepted at MPC 201

    Testing the Equivalence of Regular Languages

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    The minimal deterministic finite automaton is generally used to determine regular languages equality. Antimirov and Mosses proposed a rewrite system for deciding regular expressions equivalence of which Almeida et al. presented an improved variant. Hopcroft and Karp proposed an almost linear algorithm for testing the equivalence of two deterministic finite automata that avoids minimisation. In this paper we improve the best-case running time, present an extension of this algorithm to non-deterministic finite automata, and establish a relationship between this algorithm and the one proposed in Almeida et al. We also present some experimental comparative results. All these algorithms are closely related with the recent coalgebraic approach to automata proposed by Rutten

    Differential Hoare Logics and Refinement Calculi for Hybrid Systems with Isabelle/HOL

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    We present simple new Hoare logics and refinement calculi for hybrid systems in the style of differential dynamic logic. (Refinement) Kleene algebra with tests is used for reasoning about the program structure and generating verification conditions at this level. Lenses capture hybrid program stores in a generic algebraic way. The approach has been formalised with the Isabelle/HOL proof assistant. A number of examples explains the workflow with the resulting verification components

    Counting Complex Disordered States by Efficient Pattern Matching: Chromatic Polynomials and Potts Partition Functions

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    Counting problems, determining the number of possible states of a large system under certain constraints, play an important role in many areas of science. They naturally arise for complex disordered systems in physics and chemistry, in mathematical graph theory, and in computer science. Counting problems, however, are among the hardest problems to access computationally. Here, we suggest a novel method to access a benchmark counting problem, finding chromatic polynomials of graphs. We develop a vertex-oriented symbolic pattern matching algorithm that exploits the equivalence between the chromatic polynomial and the zero-temperature partition function of the Potts antiferromagnet on the same graph. Implementing this bottom-up algorithm using appropriate computer algebra, the new method outperforms standard top-down methods by several orders of magnitude, already for moderately sized graphs. As a first application, we compute chromatic polynomials of samples of the simple cubic lattice, for the first time computationally accessing three-dimensional lattices of physical relevance. The method offers straightforward generalizations to several other counting problems.Comment: 7 pages, 4 figure

    Respostas do cafeeiro à calagem

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    Field experiments were conducted in a stablished coffee plantation for 8 years (1975-82) on Brazilian Oxisols to investigate the effects of liming these soils (0.0,2.5, 5 and 10 tons/ha) on the soil chemical properties, production and mineral nutrition of coffee (Coffea arabica L.) trees. The soil pH, cation exchange capacity (CEC) and exchangeable Ca and Mg increased, while exchangeable AI and K decreased whith increasing dolomitic lime rates. The lime effects were limited to the top soil only (0-30 cm). Liming significantly increased leaf Ca and Mg, reduced leaf Mn (eliminated the toxic effects), Zn and K, and had no effect on leaf N, P, and Cu in the leaves. The yields of coffee were increased by reducing the exchangeable Al and by adjusting the Ca-K, Ca-Mg, and Mg-K ratios to 13:1, 4:1 and 3:1, respectively. The best coffee yields were obtained with the lowest lime rate (2.5 tons/ha). Higher lime rates (5 and 10 tons/ha) resulted in decreased yields.Experimentos de campo foram conduzidos em dois dos principais solos da região cafeeira do Paraná (LRd e LEd), por um período de 8 anos (1975-82), com o objetivo de estudar os efeitos de doses crescentes de calcário dolomítico (0, 2,5, 5,0 e 10,0 t/ha) nas propriedades químicas do solo, produção e estado nutricional do cafeeiro (Coffea arábica L.). O pH do solo, capacidade de troca de cátions (CTC) e Ca e Mg trocáveis aumentaram, enquanto que o Al e K trocáveis diminuíram com o aumento das doses de calcário. Estes efeitos foram evidentes apenas na superfície do solo (0-30 cm). Os efeitos da calagem no estado nutricional do cafeeiro foram pronunciados, em virtude do aumento nas concentrações de Ca e Mg, redução nas de Mn (eliminou os efeitos tóxicos), Zn e K e inalteração nas de N, P e Cu nos tecidos foliares. A neutralização do Al tóxico e o ajustamento das relações entre Ca-K, Ca-Mg e Mg-K para 13:1, 4:1 e 3:1, respectivamente, aumentaram a produção do cafeeiro. As melhores produções de café foram associadas com a mais baixa dose de calcário (2,5 t/ha), sendo que as mais elevadas (5 e 10 t/ha) diminuíram sistematicamente a produção do cafeeiro

    E-Beam Generated Plasma Etching for Developing High-Reflectance Mirrors for Far-Ultraviolet Astronomical Instrument Applications

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    Astronomical space telescopes to study astrophysical phenomena from the far-ultraviolet (FUV) to the near infrared (NIR) will require mirror coatings with high reflectance over this entire spectral region. While coatings for the optical and NIR part of the spectrum are fairly well developed with proven performance, the FUV presents significant challenges. The U.S. Naval Research Laboratory (NRL) has developed a processing system based on an electron beam-generated plasma that provides for controlled fluorination and/or etching of surfaces with near monolayer precision and minimal changes to surface morphology. In this paper, we report recent results of samples treated in the NRL Large Area Plasma Processing System (LAPPS) where restoration of the high intrinsic reflectance in the FUV spectral range have been observed of aluminum (Al) mirrors protected with a magnesium di-fluoride (MgF2) overcoat. This paper will also extend these studies to other Al mirrors protected with aluminum tri-fluoride (AlF3) in order to realize the high intrinsic reflectance Al down to FUV wavelengths (100200 nm), while still maintaining the high reflectance in the optical and NIR spectral regions. Laboratory test data and optical diagnostic techniques used to verify surface scattering and durability of selected coatings will be presented. Finally, we will discuss the scalability of the LAPPS etching process in order to realize these high-reflectivity coatings on mirror segments as large as those proposed for the Large Ultraviolet, Optical, and Infrared (LUVOIR) astronomical telescope system (1+meter class)

    Counterexample-Guided Polynomial Loop Invariant Generation by Lagrange Interpolation

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    We apply multivariate Lagrange interpolation to synthesize polynomial quantitative loop invariants for probabilistic programs. We reduce the computation of an quantitative loop invariant to solving constraints over program variables and unknown coefficients. Lagrange interpolation allows us to find constraints with less unknown coefficients. Counterexample-guided refinement furthermore generates linear constraints that pinpoint the desired quantitative invariants. We evaluate our technique by several case studies with polynomial quantitative loop invariants in the experiments

    Refinement algebra for probabilistic programs

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    We identify a refinement algebra for reasoning about probabilistic program transformations in a total-correctness setting. The algebra is equipped with operators that determine whether a program is enabled or terminates respectively. As well as developing the basic theory of the algebra we demonstrate how it may be used to explain key differences and similarities between standard (i.e. non-probabilistic) and probabilistic programs and verify important transformation theorems for probabilistic action systems.29 page(s
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