Automata, Computability And Complexity: Theory And .
Automata, Computability and Complexity: Theory andApplicationsElaine RichIndexα-β pruning.823Ψ(L) .235, 240ℵ0 . .615ω-automaton .88, 154 H . 338, 342, 345, 365, 367, 371 Hε .367, 380ϕk 448ε-loop.59, 65, 145 M 350 n .566, 597 P 500µ-recursive function.442, 453ε-rule.17315-puzzle .35, 569, 5762-CNF. See 2-conjunctive normal form2-conjunctive normal form .523, 5372FSMs-INTERSECT.5532-SAT .523, 537, 5602-SAT-MAX.5373-CNF. See 3-conjunctive normal form3-conjunctive normal form .498, 6363-conjunctiveBoolean .6363-SAT .498, 510, 511, 523, 6363x 1 problem.331, 4524-color problem .526A . .355, 371Aε . .356, 371A* algorithm . 570, 576, 578, 708, 794, 826AALL .356, 371Aanbn .371AANY .356, 371Aaronson, Scott .577abacus .836absorption laws .582, 605acceptingby a deterministic TM.288by a DFSM.47, 537by a nondeterministic TM.299by a PDA.194, 212, 667by an NDFSM.54access control matrix .752Ackermann, Wilhelm.318, 440, 453Ackermann’s function .440, 453active tape.280ACT-V.809Ada .701adder .839adjacency matrix.461, 592Adleman, Leonard .452, 757admissibilityof a heuristic function .573, 826of a search algorithm.574age of universe.441, 457, 838agentintelligent .737, 794, 804, 808, 825agreement in natural languages .268, 417, 784Aho, Alfred.154, 276AI See artificial intelligenceAL.820Alexander, Christopher.99ALGOL 58.697ALGOL 60.163, 697Algol 68 .701algorithm.31, 317, 619algorithms3-conjunctiveBoolean .636A* 570atmostoneEps.175buildFSMcanonicalform .74buildgrammar .208buildkeywordFSM.112buildunambiggrammar .232cfgtoPDAbottomup.203cfgtoPDAnoeps sure .608conjunctiveBoolean.636connected icted verttoGreibach .663converttononterminal.410
createOBDDfromtree.642decideCFL.242decideCFLempty .244decideCFLinfinite .244decideCFLusingGrammar .241decideCFLusingPDA .243decideFSM .146decideregex .146dfsmsimulate .64disjunctiveBoolean.637Earleyparse.272emptyFSM tyFSMsimulate.147eps.58equalFSMs .149Eulerian .488finiteFSM 76follow .276forward h.822game-search-α-β .824grammartofsm.122infiniteFSM .149intersectPDAandFSM .224Kruskal.489minDFSM.72minimalFSM .149minimax.820minimax with α-β pruning .823MSTdecide .490ndfsmconvertandsimulate .64ndfsmsimulate .59ndfsmtodfsm .60, 657obtainSelf .447PDAtoCFG .209proveFOL.382QBFdecide .549quicksort .562, 578regextofsm.104removeEps.173removeLong ve.165removeunreachable.166resolve-Boolean .639resolve-FOL.653simcomputer.302simple-rewrite .157totalFSM .147unify-for-resolution.651Viterbi .84without .228alignment of protein sequences .766allele .81, 763almost satisfiability.538alphabet .9alpha-beta pruning .823alt 240Alternating Bit protocol.63, 97, 730alternating Turing machine.819ALU.839Amazons .819ambiguityin context-free grammars170, 257, 258, 384, 390,700in English .172, 179, 700, 786in programming languages.172, 177, 701in regular grammars .171inherent .172, 384techniques for reducing.173ambiguous attachment .177, 179, 788AnBn . 16, 24, 133, 231, 235, 342, 407, 560AnBnCn25, 28, 215, 219, 288, 323, 342, 394, 403,406, 417, 425, 459, 464, 484and elimination .583and introduction.583Anderson, John R. .809Antikythera Mechanism . xii, 833antisymmetry .594AP.820APL .4Appel, Kenneth.526, 578approximation algorithm .458, 561, 820APSPACE.820Archimedes.570argmax .85, 189ARPAbet.791ARQ protocol .729artificial intelligence .6, 650, 708, 793, 825associativity .605astronomical calculator.834astronomical clock.835asymptotic dominance .466, 623, 685atmostoneEps.175, 245ATN.See augmented transition networkatoms in universe .153, 441, 820attachment ambiguity .177, 179, 788attribute grammar .416, 426, 453augmented transition network.815Austin Villa .841AutoCAD.704automatic programming.41, 709automatic reasoning.793automaton .833
average case performance.464Baader, Franz.745Bach chorales.814, 815backgammon.818Backus Naur form.16, 163, 697, 806Backus, John.697backward chaining.346, 797, 808Baker, Robert.812Bal24, 135, 155, 161, 170, 175, 178, 191, 195, 213,240, 555balanced delimiters .190, 555balanced parentheses language .See BalBandke, Volker. xiibar code .76, 96Bar-Hillel, Yehoshua .154, 276, 452Baroni, Mario .814Baum, Leonard E.154Baum-Welch algorithm .84Bel, Bernard.814beliefreasoning about .795, 804Bengal farmers.457, 577Bentley, Jon .780Berners-Lee, Tim.27, 738best-first search.570, 708, 815bidirectional finite state transducer.77, 774Big Bang.441, 457, 465, 838big-O .466, 624, 685bigram model.780bigram tagger.776bijection .604binary adder .22, 839binary decision tree.641binary function.602binary multiplier .839binary relation.591binary search.760BIN-PACKING .510, 539bipartite graph.526, 681bisection of a graph.539Bishop, Matt .753BNF .See Backus Naur formBoolean expression grammar .191, 844Boolean logic.581, 635decidability .381normal forms.635resolution .537, 638satisfiability36, 314, 381, 459, 497, 504, 581, 638,641bottom-up parser.202, 259, 419bounded simulation.147BOUNDED-PCP .378, 511, 537boustrophedon .386BPP.564Brachman, Ronald .745, 795branching factor of a grammar169, 180, 216, 233,244, 671breadth-first search .301, 479, 573, 675, 679Bryant, Randal.642Büchi automaton.88, 154, 717, 728Büchi, J. .154buildFSMcanonicalform.74, 146, 149buildgrammar .208buildkeywordFSM.112, 154, 473, 768buildunambiggrammar .232business rules engine .806, 809busy beaver function.292, 433, 441, 453C 12, 177C .177, 363Cage, John .811Camilleri, Lelio.814canonical form .74, 180for Boolean expressions.74, 643for FSMs .74, 146Cantor, David .452cardinalityof a language.13of a set.587of the context-free languages .215of the regular languages .127of the SD languages .336Carmichael number.567Cartesian product.590causal universe.153, 335, 441, 820ceiling .32cellular automaton .319, 324, 419certificate .493CFG .See context-free grammarCFGALL .385, 387cfgtoPDAbottomup .202, 203, 245cfgtoPDAnoeps .242, 246cfgtoPDAtopdown.201, 202, 242, 245, 388CFL .See context-free languageChampandard, Alex .825Chandra, Ashok .820characteristic function.11, 291, 433, 587chart parser . See parser, chartchatbot .793, 831checkers .575, 818chemical structure matching .510chess . 7, 503, 534, 575, 815, 818Chinese room argument.793Chomsky hierarchy.154, 275, 393, 416, 452Chomsky normal form180, 182, 191, 222, 240, 241,248, 260, 275, 410, 661Chomsky, Noam . 12, 154, 275, 416, 452, 814chop .39, 140, 239CHORAL.815Christofides, Nicos .577chromatic XE "graph:chromatic number" number536chromatic number .501, 526
CHROMATIC-NUMBER.501, 526, 536chromosome .763Church, Alonzo.318, 319, 320, 452, 704Church's thesis . See Church-Turing thesisChurch-Turing thesis .317, 318, 329, 397circuitEulerian.487, 499, 523, 536, 736Hamiltonian .494, 510, 515, 523CKY algorithmSeeCocke-Kasami-YoungeralgorithmClarke, Edmund .154, 713clausedefinite .799Horn .798in Boolean logic .498, 635in first order logic .645clause form .585, 646Cline, Alan. xiiCLIQUE . 494, 497, 499, 501, 510, 537clique detection.494, 497, 501, 510, 537clockmechanical .835Clocksin, William F.801closed world assumption .744, 803closuremathematical definition .40, 607, 625programming language definition.707closure propertiesinfinite languages.42closure properties ofBüchi automata .92, 718context-free languages199, 221, 226, 237, 239,276context-sensitive languages .410, 426, 453, 558decidable languages .337, 342deterministic context-free languages 228, 240, 666finite languages .40, 42infinite languages.40PSPACE.559regular languages .52, 129, 139, 142semidecidable languages.337, 343space complexity classes.558, 559the class BPP.564the class L .557the class NP.528, 537the class P .483, 537CNF .See conjunctive normal form2-CNF . See 2-conjunctive normal form3-CNF . See 3-conjunctive normal formCobol .187Cocke, J. .260, 276Cocke-Kasami-Younger algorithm241, 247, 260,276, 477, 485, 786codomain of a function .601co-dspace.558coffee can problem .621co-finite language .540cognitive modeling .806, 808, 827cognitive psychology.806, 808, 827Cohn, Martin.153co-L .557Colbourn, Charles.817coloring. See map coloringcolorless green ideas.12, 788Common Music .704commutativity.605compiler construction 5, 172, 247, 275, 364, 372, 697complementclosure under52, 129, 222, 228, 337, 413, 483,528, 557, 558, 564of a language.14, 330, 366of sets .606complement of sets .589complementary literals .639, 652complementdetPDA .246complete graph .526completenesslogical .585of a set of inference rules .582with respect to a world.586completeness of a set ofinference rules.585Completeness Theorem .318, 382, 451, 585, 586complexitylogarithmic space .555multitape Turing machines .298nondeterministic Turing machines.298, 301polynomial space .544polynomial time .483randomized Turing machines.563space .463, 541sublinear space.554time .463, 483, 623Complexity Zoo.459, 577COMPOSITES .299, 491, 523, 566composition of functions .602composition of relations .592compositional semantics.16, 99, 419compression algorithm .691computable function . 291, 319, 400, 430, 437, 441computationof a Turing machine.284of an FSM .47of an LBA .406of an PDA .194computation history .385, 414computational biology .6, 750, 761Computer Cantata .812computer game .7, 570, 808, 824computer network .727computetransitiveclosure.608concatenation
closure under.129, 221, 342, 411of languages .14of strings .9concept subsumption .599concurrent systems .74, 89, 713co-ndspace.558configurationof a PDA .193of a Turing machine.283of an FSM .47conflict resolution .808conjunctive normal formfor Boolean logic .498, 635, 638for first-order logic.645, 796conjunctiveBoolean .636co-NL.557CONNECTED.21, 460, 484, 485, 541connected graph.21, 484, 485co-NP.528, 566consistency .586construction proof. See proof by constructioncontext-free grammar .160, 813ambiguity .170, 390correctness proof.166designing.164for English .See English grammarfor programming languages .697for URIs .739island.723island.186LL(1).257LR(1) .267normal form .180simplifying.165stochastic.188, 771, 788, 789context-free language . 24, 155, 161, 485, 699, 781deterministic .201, 227, 231, 258, 666inherently ambiguous.172, 231, 384LL(1).258LR(k).267undecidable properties .384context-free parsing169, 201, 230, 247, 477, 480, 485context-free Pumping TheoremSeePumpingTheorem, context-freecontext-sensitive grammar.393, 407, 814context-sensitive language.405, 452, 554, 558contradictionin Boolean logic .583in first-order logic .586contradiction proof .See proof by contradictionconvertPDAtodetnormalform .670convertpdatorestricted.205, 246, 668converttoChomsky .182, 245converttoclauseform .647converttoGreibach .663, 666converttononterminal.410Conway, John .319, 324, 452Cook, Stephen.504, 577Cook-Levin Theorem .504, 505, 577, 796Cope, David.815Coppersm
Automata, Computability and Complexity: Theory
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