31 research outputs found

    Tools and Algorithms for the Construction and Analysis of Systems

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    This open access book constitutes the proceedings of the 28th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2022, which was held during April 2-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 46 full papers and 4 short papers presented in this volume were carefully reviewed and selected from 159 submissions. The proceedings also contain 16 tool papers of the affiliated competition SV-Comp and 1 paper consisting of the competition report. TACAS is a forum for researchers, developers, and users interested in rigorously based tools and algorithms for the construction and analysis of systems. The conference aims to bridge the gaps between different communities with this common interest and to support them in their quest to improve the utility, reliability, exibility, and efficiency of tools and algorithms for building computer-controlled systems

    Automated Deduction – CADE 28

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    This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions

    Proceedings of the 21st Conference on Formal Methods in Computer-Aided Design – FMCAD 2021

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    The Conference on Formal Methods in Computer-Aided Design (FMCAD) is an annual conference on the theory and applications of formal methods in hardware and system verification. FMCAD provides a leading forum to researchers in academia and industry for presenting and discussing groundbreaking methods, technologies, theoretical results, and tools for reasoning formally about computing systems. FMCAD covers formal aspects of computer-aided system design including verification, specification, synthesis, and testing

    Aspects of p-adic computation

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    Subfields of Solvable Sextic Field Extensions

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    Let F be a field, f(x) in F[x] an irreducible polynomial of degree six, K the stem field of f, and G the Galois group of f over F. We show G is solvable if and only if K/F has either a quadratic or cubic subfield. We also show that G can be determined by: the size of the automorphism group of K/F, the discriminant of f, and the discriminants of polynomials defining intermediate fields. Since most methods for computing polynomials defining intermediate subfields require factoring f over its stem, we include a method that does not require factorization over K, but rather only relies factoring two linear resolvent polynomials over F

    Mixed Degree Number Field Computations

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    We present a method for computing complete lists of number fields in cases where the Galois group, as an abstract group, appears as a Galois group in smaller degree. We apply this method to find the 25 octic fields with Galois group PSL₂(7) and smallest absolute discriminant. We carry out a number of related computations, including determining the octic field with Galois group 2³:GL₃(2) of smallest absolute discriminant
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