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What Can Be Computed? is a uniquely accessible yet rigorous introduction to the most profound ideas at the heart of computer science. Crafted specifically for undergraduates who are studying the subject for the first time, and requiring minimal prerequisites, the book focuses on the essential fundamentals of computer science theory and features a practical approach that uses real computer programs (Python and Java) and encourages active experimentation. It is also ideal for self-study and reference. The book covers the standard topics in the theory of computation, including Turing machines and finite automata, universal computation, nondeterminism, Turing and Karp reductions, undecidability, time-complexity classes such as P and NP, and NP-completeness, including the Cook-Levin Theorem. But the book also provides a broader view of computer science and its historical development, with discussions of Turing's original 1936 computing machines, the connections between undecidability and Gödel's incompleteness theorem, and Karp's famous set of twenty-one NP-complete problems. Throughout, the book recasts traditional computer science concepts by considering how computer programs are used to solve real problems. Standard theorems are stated and proven with full mathematical rigor, but motivation and understanding are enhanced by considering concrete implementations. The book's examples and other content allow readers to view demonstrations of--and to experiment with--a wide selection of the topics it covers. The result is an ideal text for an introduction to the theory of computation.

Informática --- Informática --- Informática --- Programación de ordenadores --- Historia --- Filosofía --- AKS primality test. --- AND gate. --- ASCII. --- Addition. --- Algorithm. --- Asymptotic analysis. --- Axiom. --- Binary search algorithm. --- Boolean satisfiability problem. --- C0. --- Calculation. --- Church–Turing thesis. --- Combinatorial search. --- Compiler. --- Complexity class. --- Computability theory. --- Computability. --- Computable function. --- Computable number. --- Computation. --- Computational model. --- Computational problem. --- Computer program. --- Computer. --- Computers and Intractability. --- Computing. --- Conditional (computer programming). --- Counting. --- Decision problem. --- Deterministic finite automaton. --- Elaboration. --- Entscheidungsproblem. --- Equation. --- Exponentiation. --- FNP (complexity). --- Factorization. --- For loop. --- Function problem. --- Halting problem. --- Hilbert's program. --- Indent style. --- Instance (computer science). --- Instruction set. --- Integer overflow. --- Integer. --- Interpreter (computing). --- Iteration. --- List comprehension. --- Mathematical induction. --- Model of computation. --- NP (complexity). --- NP-completeness. --- NP-hardness. --- Notation. --- OR gate. --- Optimization problem. --- P versus NP problem. --- Permutation. --- Polylogarithmic function. --- Polynomial. --- Potential method. --- Primality test. --- Prime number. --- Program analysis. --- Pseudocode. --- Pumping lemma. --- Python (programming language). --- Quantifier (logic). --- Quantum algorithm. --- Radix sort. --- Random-access machine. --- Recursive language. --- Regular expression. --- Rice's theorem. --- Rule 110. --- Schematic. --- Search problem. --- Set (abstract data type). --- Simulation. --- Snippet (programming). --- Solution set. --- Solver. --- Source code. --- Special case. --- State diagram. --- Statement (computer science). --- Subsequence. --- Subset. --- Summation. --- Theory of computation. --- Thread (computing). --- Time complexity. --- Transition function. --- Tseytin transformation. --- Turing machine. --- Turing reduction. --- Turing test. --- Turing's proof. --- Variable (mathematics). --- Workaround.