Predicate calculus and program semantics
Predicate calculus and program semantics
Categorical methods in computer science with aspects from topology
Categorical methods in computer science with aspects from topology
Topology and category theory in computer science
Topology and category theory in computer science
Semantics of programming languages: structures and techniques
Semantics of programming languages: structures and techniques
Introduction to Computability
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A Mathematical Theory of Communication
A Mathematical Theory of Communication
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We present the background and justification for a new approach to studying computation and computational complexity. We focus on categories of problems and categories of solutions which provide the logical definition on which to base an algorithm. Computational capability is introduced via a formalization of computation termed a model of computation. The concept of algorithm is formalized using the methods of Traub, Wasilkowski and Woźniakowski, from which we can formalize the differences between deterministic, non-deterministic, and heuristic algorithms. Finally, we introduce our measure of complexity: the Hartley entropy measure. We provide many examples to amplify the concepts introduced.