Full Description
Logic and Complexity looks at basic logic as it is used in Computer Science, and provides students with a logical approach to Complexity theory. With plenty of exercises, this book presents classical notions of mathematical logic, such as decidability, completeness and incompleteness, as well as new ideas brought by complexity theory such as NP-completeness, randomness and approximations, providing a better understanding for efficient algorithmic solutions to problems.
Divided into three parts, it covers:
- Model Theory and Recursive Functions - introducing the basic model theory of propositional, 1st order, inductive definitions and 2nd order logic. Recursive functions, Turing computability and decidability are also examined.
- Descriptive Complexity - looking at the relationship between definitions of problems, queries, properties of programs and their computational complexity.
- Approximation - explaining how some optimization problems and counting problems can be approximated according to their logical form.
Logic is important in Computer Science, particularly for verification problems and database query languages such as SQL. Students and researchers in this field will find this book of great interest.
Contents
1. Basic model theory and computability.- 1. Propositional logic.- 2. Deduction systems.- 3. First-order logic.- 4. Completeness of first order logic.- 5. Models of computation.- 6. Recursion and decidability.- 7. Incompleteness of Peano arithmetic.- 2. Descriptive Complexity.- 8 Complexity: time and space.- 9. First-order definability.- 10. Inductive definitions and second-order logic.- 11. Time complexity : the classes P and NP.- 12. Models of parallel computations.- 13. Space complexity: the classes L, FL, NL and PSPACE.- 14. Definability of optimization and counting problems.- 3. Approximation and classes beyond NP.- 15. Probabilistic Classes.- 16. Probabilistic verification.- 17. Approximation.- 18. Classes beyond NP.- List of Figures.
