H halting problem, 179. homomorphism, 154

Transcription

1 215 A accept, 23, 28, 120, 132, 160 acceptance by empty stack, 127 acceptance by final states, 128 accepting state, 23 algorithm, 178, 179 alphabet, 4 ambiguous, 99 automaton, 1 B Backus normal form, 84 Backus-Naur form, 84 basis, 10 binary relation, 9 Boolean operation, 73 bottom-up parsing, 98 bottom-up parsing, 143 boundary symbol, 157 C cell, 24, 157 Chomsky hierarchy, 169 Chomsky normal form: CNF, 105 Church s hypothesis, 171 CKY algorithm, CKY 138 class, 8 closure, 58 closure property, 73 comparison tree, 33 complement, 7 computable, 171 concatenation, 3, 57 configuration, 118, 125, 159 context-free grammar: CFG, 93 context-free language: CFL, 95 context-sensitive grammar: CSG, 166 context-sensitive language: CSL, 166 D De Morgan s law, 7 dead state, 43 dead symbol, 100 decidable, 179 decision algorithm, 179 decision problem, 179 derivation diagram, 167 derivation tree, 96 derive, 87, 94 deterministic finite automaton: DFA, 24 deterministic language: DL, 129 deterministic pushdown automaton: DPDA, 124 deterministic pushdown transducer: DPDT, 131 difference, 7 direct product, Cartesian product, 7, 176 directly derive, 86, 94, 155 directly left-recursive, 107 dynamic programming: DP, 138 著作権 : 森北出版株式会社

2 216 E edge, 9 edge, 9 effective procedure, 178 element, 5 emptiness problem, 102 empty, 30 empty sequence, 3 empty set, 5 empty string, 3 endmarker symbol, 123 enumerate, 169 ε-closure, ε- 52 ε-free, ε- 102 ε-mode, ε- 126 ε-move, ε- 50 ε-production, ε- 102 ε-rule, ε- 126 ε-transition, ε- 50, 126 equivalence relation, 9 equivalent, 22, 29, 61, 88 F family, 8 family of languages, 72 final state, 23 finer, 41 finite automaton: FA, 24 finite set, 5 finite state automaton: FSA, 24 finite state language, 28 formal grammar, 82 formal language, 2 G generalized nondeterministic finite automaton: GNFA, 66 generate, 87 Greibach normal form: GNF, 107 H halting problem, 179 handle, 143 height, 118, 125 Hilbert s tenth problem, homomorphism, 154 I induction, inductive proof, 10 inductive conclusion, 11 inductive hypothesis, 10 inductive step, 10 infinite set, 5 inherently ambiguous, 99 initial configuration, 118, 125, 158 initial instantaneous description, 158 initial stack symbol, 118 initial state, 14, 23 initial symbol, 82 input, 1, 14 input sequence, 2 input string, 2 input symbol, 2 instance, 178 instance, 178 instantaneous description: ID, 159 internal node, 10 internal state, 14 intersection, 7 isomorphic, 36 K k-equivalent, k- 37 Kleene closure, 58 L labeled tree, 9 language, 4 language accepted, 28

3 217 language generated, 87 language over Σ, Σ 4 language recognized, 28 leaf, 10 left-linear grammar, 91 left-recursive, 107 leftmost derivation, 94 length, 3, 10 lexical analyzer, 14 linear bounded automaton: LBA, 168 linear bounded automaton: LBA, 168 live symbol, 100 LL(k) grammar, LL(k) 142 LR(k) grammar, LR(k) 144 M mathematical language, 2 Mealy machine, 15 membership problem, 136 minimal form, reduced form, 36 mode, 125 monotonic grammar, 166 Moore machine, 17 move, 119, 126, 158 multitape TM, 161 mutually disjoint, 7 Myhill-Nerode s theorem, 41 N natural language, 2 next move function, 158 node, vertex, 9 non-context-free language, 148 nondeterministic finite automaton with ε-moves, ε- 51 nondeterministic finite automaton: NFA, 45 nondeterministic pushdown automaton: NPDA, 131 nondeterministic TM, 162 non-regular language, 74 nonterminal symbol, 82 nullable symbol, 102 O offspring, son, 10 one-way, 25 output, 1, 14 output function, 15, 17 P parent, father, 10 parse tree, 97 parsing, syntax analysis, 98, 137 partially computable, 171 path, 10 pattern automaton, 76 pattern matching, 76 pattern matching, 76 phrase structure grammar: PSG, 155 phrase structure language: PSL, 156 pop up, 117 positive star closure, 59 Post s Correspondence Problem: PCP, 181 power set, 8 prefix, 3 prefix property, 122 procedure, 178 product, 7 production, 82 programming language, 2 proper, 3 Pumping Theorem, 114 Pumping Theorem, 113 push down, 117

4 218 pushdown stack, 116 pushdown symbol, 117 pushdown tape, 117 R reachable, 30, 101 reading mode, 126 real-time, 126 recognizer, 23 recursive, 169 recursive, 107 recursively enumerable, 168 reduce, 143 reduced, 104 reduction, 182 reflexive law, 9 regular expression, 60 regular expression, 60 regular grammar: RG, 85 regular grammar: RG, 85 regular language: RL, 28 regular language: RL, 28 regular set, 60 regular set, 60 reject, 28 reversal, 121 rewriting rule, 82 right invariant, 40 right-linear grammar, 90 right-recursive, 107 rightmost derivation, 95, 144 root, 9 S self-embedding, 112 sentence, 2, 82, 87, 95, 156 sentential form, 87, 94, 156 sequence, 3 sequential machine, 14 set, 5 simple, 130 simple deterministic grammar, 115 simple deterministic language: SDL, 115, 122 simple deterministic pushdown automaton: simple DPDA, 118 simple language, 122 simplification, 23 solvable, 136, 179 stack, 117 stack symbol, 117 star closure, 3, 58 start symbol, 82 state, 14 state transition, 14, 26 state transition diagram, 16, 17, 25, 45 state transition function, 15 state transition table, 15, 17, 25, 46 strict, 127 string, 3 string over Σ, Σ 3 subset, 6 subset construction, 48 substring, 3 subtree, 10 suffix, 3 symmetric law, 9 syntactic structure, 97 syntactic variable, 82 T terminal configuration, 159 terminal symbol, 82 TM with a one-way infinite tape, 161 top-down parsing, 98 top-down parsing, 142 transducer, 23 transition diagram, 120 transition rule, 118 transition, derivation, 119, 126, 127 transitive law, 9

5 219 tree, 9 Turing machine: TM, 157 type 0 grammar, type 1 grammar, type 2 grammar, 2 93 type 3 grammar, 3 85 U unambiguous, 99 undecidable, 179 union, 6 unit production, single production, 103 universal set, 7 universal set, 7 universal Turing machine: UTM, 171, 174 unsolvable, 179 useless symbol, 100 uvwxy-theorem, uvwxy- 114 V Venn diagram, 8 W word, 4 Y Yes-No problem, Yes-No 178