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5644 results in Programming Languages and Applied Logic

Page 28 of 283

Complexity of Infinite-Domain Constraint Satisfaction
  • Manuel Bodirsky
  • Published online:
    28 May 2021
    Print publication:
    10 June 2021
  • Constraint Satisfaction Problems (CSPs) are natural computational problems that appear in many areas of theoretical computer science. Exploring which CSPs are solvable in polynomial time and which are NP-hard reveals a surprising link with central questions in universal algebra. This monograph presents a self-contained introduction to the universal-algebraic approach to complexity classification, treating both finite and infinite-domain CSPs. It includes the required background from logic and combinatorics, particularly model theory and Ramsey theory, and explains the recently discovered link between Ramsey theory and topological dynamics and its implications for CSPs. The book will be of interest to graduate students and researchers in theoretical computer science and to mathematicians in logic, combinatorics, and dynamics who wish to learn about the applications of their work in complexity theory.

  • 4 - Model Checking Quantum Automata

  • Mingsheng Ying, University of Technology, Sydney, Yuan Feng, University of Technology, Sydney
  • Book:
    Model Checking Quantum Systems
    Published online:
    14 January 2021
    Print publication:
    04 February 2021, pp 50-86

  • Summary

    Quantum systems are modelled as different mathematical structures, depending on their nature and complexity. This chapter considers one of the simplest (discrete-time) models of quantum systems, namely quantum automata. It introduces a way of describing linear-time (dynamic) properties of quantum systems and presents several algorithms for checking certain linear-time properties of quantum automata, for example, invariants andreachability.

  • 2 - Basics of Model Checking

  • Mingsheng Ying, University of Technology, Sydney, Yuan Feng, University of Technology, Sydney
  • Book:
    Model Checking Quantum Systems
    Published online:
    14 January 2021
    Print publication:
    04 February 2021, pp 6-30

  • Summary

    Model checking is an algorithmic technique for verification of computing and communication hardware and software. This book extends the technique of model checking for quantum systems. As preliminaries, this chapter introduces basics of model checking for both classical non-probabilistic and probabilistic systems.

  • 5 - Model Checking Quantum Markov Chains

  • Mingsheng Ying, University of Technology, Sydney, Yuan Feng, University of Technology, Sydney
  • Book:
    Model Checking Quantum Systems
    Published online:
    14 January 2021
    Print publication:
    04 February 2021, pp 87-137

  • Summary

    This chapter develops model-checking techniques for a much larger class of quantum systems modelled as quantum Markov chains or more generally, quantum Markov decision processes. The differences between quantum automata and quantum Markov systems require us to develop algorithms for the latter that are fundamentally different from those for the former.

Page 28 of 283