Computational theory is the basis of computer application, theory and applications are missing one.
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C01 automata C02 with poor automata C03 regular expressions and regular languages C04 the nature of regular language C05 context-independent grammar and context-independent language C06 push automata C07 Context-independent language C08 Turing machine C09 non-deterministic C10 difficult to solve problems C11 other problem classes---- C01 Automatic Machine----
- There are poor automata Two important factors (FA) are state and Jump , State is data/environment, jump is function/response.
- There are two kinds of the structure representation of automata, one is regular expression , the regular expression (RE) and the finite automaton (FA) are equivalent, the former is only the latter's structural notation, the other is grammar , usually refers to the context- Independent grammar , which is used to build the compiler parser.
- can be judged qualitative is what the computer can do what not to do, the problem that the computer can solve is called " can be judged ", and vice versa is " not determined ", difficult to solve Whether the problem is difficult to solve is easy or complex, the complexity of the polynomial is called " easy to solve "/" computable " (p problem ), and vice versa is " difficult to solve"/" Non-computable "(NP problem ).
- The proof is divided into deductive proof and inductive proof, deductive proof is based on derivation (premise and conclusion) of the propositional tree, " if so " is unidirectional, " when and only if " is bidirectional, proposition When and only if the inverse of the proposition (if A is not a b<-> B is not a), the rebuttal method (proving a and non-B contradiction) is based on this, the inverse of the law is used to overturn the wrong proposition, inductive proof is divided into the initial part (S (0) established) and derivation section (s (n) established->s (n+1)), the structural induction is based on recursive definition , so-called "structure" refers to a recursive definition of the structure. From the philosophical point of view, deduction and induction are two different processes, the former is from general to individual application process, the latter is from the individual to the general summary process, and the deduction we emphasize here is to find the premise and conclusion of the link between the path, induction is from the part to the whole , from easy to difficult recursive derivation.
- The central concept of automata theory is the alphabet, strings and languages, the alphabet (A) is the set of letters, the string (S) is the sequence of letters, the language (L) is a set of strings, the question of determining is an issue that determines whether a string belongs to a language.
Introduction to automata theory, language and computation by John E. hopcroft
