31 research outputs found
Tools and Algorithms for the Construction and Analysis of Systems
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
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
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
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Quantum Information Processing using the Power-of-SWAP
This project is a comprehensive investigation into the application of the exchange interaction,
particularly with the realization of the SWAP^1/n quantum operator, in quantum information
processing. We study the generation, characterization and application of entanglement in such
systems. Given the non-commutativity of neighbouring SWAP^1/n gates, the mathematical
study of combinations of these gates is an interesting avenue of research that we have
explored, though due to the exponential scaling of the complexity of the problem with the
number of qubits in the system, numerical techniques, though good for few-qubit systems, are
found to be inefficient for this research problem when we look at systems with higher number
of qubits. Since the group of SWAP^1/n operators is found to be isomorphic to the symmetric
group Sn, we employ group-theoretic methods to find the relevant invariant subspaces
and associated vector-states. Some interesting patterns of states are found including onedimensional invariant subspaces spanned by W-states and the Hamming-weight preserving
symmetry of the vectors spanning the various invariant subspaces. We also devise new
ways of characterizing entanglement and approach the separability problem by looking at
permutation symmetries of subsystems of quantum states. This idea is found to form a
bridge with the entanglement characterization tool of Peres-Horodecki’s Partial Positive
Transpose (PPT), for mixed quantum states. We also look at quantum information taskoriented ‘distance’ measures of entanglement, besides devising a new entanglement witness
in the ‘engle’. In terms of applications, we define five different formalisms for quantum
computing: the circuit-based model, the encoded qubit model, the cluster-state model,
functional quantum computation and the qudit-based model. Later in the thesis, we explore
the idea of quantum computing based on decoherence-free subspaces. We also investigate
ways of applying the SWAP^1/n in entanglement swapping for quantum repeaters, quantum
communication protocols and quantum memory.Trinity Barlow Scholarship by Trinity College (University of Cambridge), Nehru Bursary by Nehru Trust for Cambridge University, Hitachi CASE Grant by Hitachi-Cavendish Laboratory, Grants from Semiconductor Physics (SP) and Thin Film Magnetism (TFM) Groups, Cavendish Laboratory, University of Cambridg
Subfields of Solvable Sextic Field Extensions
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
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