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The Brock family's understanding was that the machine was made by a French inventor named Maelzel, and that it had been acquired in France. When they donated the Automaton to The Franklin Institute, the descendants of John Penn Brock knew it had been ruined in a fire and hadn't run for years. This Automaton, known as the "Draughtsman-Writer," is one such machine. The first complex machines produced by man were called "automata." The greatest and most fascinating mechanisms were those that could do things in imitation of living creatures. WATCH: Ingenious: The Evolution of Innovationĭuring the 18th century, people were in a state of wonder over mechanism.Harry Potter: The Exhibition - NOW OPEN!.The purpose of these notes is to introduce some of the basic notions of the theory of computation, including concepts from formal languages and automata theory, the theory of computability, some basics of recursive function theory, and an introduction to complexity theory. 391Ĭhapter 1 Introduction The theory of computation is concerned with algorithms and algorithmic systems: their design and representation, their completeness, and their complexity. 390 16.3 Type-0 Grammars and Context-Sensitive Grammars. 389 16.2 Derivations and Type-0 Languages. 385 16 Phrase-Structure and Context-Sensitive Grammars 389 16.1 Phrase-Structure Grammars.
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ġ5.5 Algorithms for Computing Powers Modulo m. 15.3 Modular Arithmetic, the Groups Z/nZ, (Z/nZ)∗ 15.4 The Lucas Theorem Lucas Trees. ġ5 Primality Testing is in N P 15.1 Prime Numbers and Composite Numbers. 14.3 Succinct Certificates, coN P, and EX P. ġ4 Some N P-Complete Problems 14.1 Statements of the Problems. 13.5 Propositional Logic and Satisfiability. 307ġ3 Computational Complexity P and N P 13.1 The Class P. 304 More Undecidable Properties of Languages. 303 Some Undecidability Results for CFG’s. Post Correspondence Problem Applications 303 The Post Correspondence Problem. 294 11.3 Some Applications of the DPRM Theorem. 291 11.2 Diophantine Sets and Listable Sets. ġ1 Listable and Diophantine Sets Hilbert’s Tenth 291 11.1 Diophantine Equations Hilbert’s Tenth Problem.
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10.3 Listable (Recursively Enumerable) Sets. ġ0 Elementary Recursive Function Theory 10.1 Acceptable Indexings. A Simple Function Not Known to be Computable A Non-Computable Function Busy Beavers. ĩ Universal RAM Programs and the Halting Problem 239 9.1 Pairing Functions. 8.6 Computably Enumerable and Computable Languages 8.7 The Primitive Recursive Functions. 8.5 Turing-computable functions are RAM-computable. 8.4 RAM-computable functions are Turing-computable. in the Presence of 7.11 LR(1)-Characteristic Automata. 7.8 More on LR(0)-Characteristic Automata. 7.5 The Graph Method for Computing Fixed Points. 7.4 The Intuition Behind the Shift/Reduce Algorithm. Least Fixed-Points and the Greibach Normal Form Tree Domains and Gorn Trees. Context-Free Languages as Least Fixed-Points. Useless Productions in Context-Free Grammars. 5.12 A Fast Algorithm for Checking State Equivalence. 5.10 State Equivalence and Minimal DFA’s.
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5.8 Right-Invariant Equivalence Relations on Σ∗. 5.6 Regular Expressions and Regular Languages. 5.4 The Closure Definition of the Regular Languages. ĥ Regular Languages, Minimization of DFA’s 5.1 Morphisms, F -Maps, B-Maps and Homomorphisms of DFA’s 5.2 Directed Graphs and Paths. 4.2 The Viterbi Algorithm and the Forward Algorithm. Ĥ Hidden Markov Models (HMMs) 4.1 Hidden Markov Models (HMMs). 3.6 Finite State Automata With Output: Transducers 3.7 An Application of NFA’s: Text Search. 3.3 Nondeteterministic Finite Automata (NFA’s). ģ DFA’s, NFA’s, Regular Languages 3.1 Deterministic Finite Automata (DFA’s). Please, do not reproduce without permission of the author December 21, 2018Ģ Basics of Formal Language Theory 2.1 Alphabets, Strings, Languages. Introduction to the Theory of Computation Some Notes for CIS511 Jean Gallier Department of Computer and Information Science University of Pennsylvania Philadelphia, PA 19104, USA e-mail: c Jean Gallier