Computability complexity and Languages- Fundamentals of Theoretical Computer Science

Recommendations

Info

AcknowledgmentsIt is a pleasure to acknowledge the help we have received. CharleneHerring, Debbie Herring, Barry Jacobs, and Joseph Miller made theirstudent classroom notes available to us. James Cox, Keith Harrow, SteveHenkind, Karen Lemone, Colm O'Dunlaing, and James Robinett providedhelpful comments and corrections. Stewart Weiss was kind enough toredraw one of the figures. Thomas Ostrand, Norman Shulman, LouisSalkind, Ron Sigal, Patricia Teller, and Elia Weixelbaum were particularlygenerous with their time, and devoted many hours to helping us. We areespecially grateful to them.Acknowledgments to Corrected PrintingWe have taken this opportunity to correct a number of errors. We aregrateful to the readers who have called our attention to errors and whohave suggested corrections. The following have been particularly helpful:Alissa Bernholc, Domenico Cantone, John R. Cowles, Herbert Enderton,Phyllis Frankl, Fred Green, Warren Hirsch, J. D. Monk, Steve Rozen, andStewart Weiss.xvii
xviiiAcknowledgmentsAcknowledgments to Second EditionYuri Gurevich, Paliath Narendran, Robert Paige, Carl Smith, and particularlyRobert McNaughton made numerous suggestions for improving thefirst edition. Kung Chen, William Hurwood, Dana Latch, Sidd Puri,Benjamin Russell, Jason Smith, Jean Toal, and Niping Wu read a preliminaryversion of Part 5.
Page 2 and 3: Second EditionComputability,Complex
Page 4: To the memory of Helen and Harry Da
Page 7 and 8: viiiContents3 Primitive Recursive F
Page 9 and 10: XContents11 Context-Sensitive Langu
Page 12 and 13: PrefaceTheoretical computer science
Page 14: PrefaceXValso be read immediately f
Page 20 and 21: 1Preliminaries1. Sets and n-tuplesW
Page 22 and 23: 2. Functions 3S 1 X S 2 X ••·
Page 24 and 25: 4. Predicates 5If u E A*, we write
Page 26 and 27: 5. Quantifiers 7Thus, let P(t, x 1
Page 28 and 29: 7. Mathematical Induction 9has no s
Page 30 and 31: 7. Mathematical Induction 11be prov
Page 32: 7. Mathematical Induction13Letmax(
Page 36 and 37: 2Programs andComputable Functions1.
Page 38 and 39: 2. Some Examples of Programs 19If t
Page 40 and 41: 2. Some Examples of Programs 21the
Page 42 and 43: 2. Some Examples of Programs 23was
Page 44 and 45: 3. Syntax 25Exercises1. Write a pro
Page 46 and 47: 3. Syntax 27Suppose we have a progr
Page 48 and 49: 4. Computable Functions 29together
Page 50 and 51: 4. Computable Functions 31Computabi
Page 52 and 53: 5. More about Macros 33Let f(x 1 ,
Page 54 and 55: 5. More about Macros 35Hence predic
Page 56: 5. More about Macros37an arbitrary
Page 59 and 60: 40 Chapter 3 Primitive Recursive Fu
Page 65 and 66:
46 Chapter 3 Primitive Recursive Fu
Page 67 and 68:
Page 69 and 70:
Page 71 and 72:
Page 73 and 74:
Page 75 and 76:
Page 77 and 78:
Page 79 and 80:
Page 81 and 82:
Page 84 and 85:
4A Universal Program1. Coding Progr
Page 86 and 87:
1. Coding Programs by Numbers 67The
Page 88 and 89:
2. The Halting Problem 69numbers ca
Page 90 and 91:
3. Universality 71In considering th
Page 92 and 93:
3. UniversalityZ <-Xn+l + 1ns <---
Page 94 and 95:
3. Universality 75Now we can define
Page 96 and 97:
3. Universality 77recursion. Finall
Page 98 and 99:
4. Recursively Enumerable Sets 79We
Page 100 and 101:
4. Recursively Enumerable Sets81[A]
Page 102 and 103:
4. Recursively Enumerable Sets 83Pr
Page 104 and 105:
5. The Parameter Theorem857. Let A,
Page 106 and 107:
5. The Parameter Theorem 87using fi
Page 108 and 109:
6. Dlagonalization and Reducibility
Page 110 and 111:
6. Diagonalization and Reducibility
Page 112 and 113:
6. Diagonalization and Reducibility
Page 114 and 115:
7. Rice's Theorem 95Show that Q(x)
Page 116 and 117:
8. The Recursion Theorem 97thesis.
Page 118 and 119:
8. The Recursion Theorem 99After th
Page 120 and 121:
8. The Recursion Theorem 101know if
Page 122 and 123:
8. The Recursion Theorem 103and con
Page 124 and 125:
9. A Computable Function That Is No
Page 126 and 127:
Page 128 and 129:
Page 130 and 131:
Page 132 and 133:
5Calculations on Strings1. Numerica
Page 134 and 135:
1. Numerical Representation of Stri
Page 136 and 137:
Page 138 and 139:
Page 140 and 141:
2. A Programming Language for Strin
Page 142 and 143:
Page 144 and 145:
Page 146 and 147:
3. The Languages .9" and .5';, 127W
Page 148 and 149:
4. Post- Turing Programs 1294. Post
Page 150 and 151:
4. Post-Turing Programs 131Of cours
Page 152 and 153:
4. Post- Turing Programs133[C) RIGH
Page 154 and 155:
5. Simulation of .9';, in fT 1354.
Page 156 and 157:
--------'5. Simulation of Y, In .'T
Page 158 and 159:
5. Simulation of .9';, In !T 139cor
Page 160 and 161:
6. Simulation of .9'" in .'7' 1413.
Page 162 and 163:
6. Simulation of .'T in .'7'143Simi
Page 164 and 165:
6Turing Machines1. Internal StatesN
Page 166 and 167:
1. Internal States147Table 1.1Symbo
Page 168 and 169:
1. Internal States 149and the final
Page 170 and 171:
1. Internal States151[Ad IF s 0 GOT
Page 172 and 173:
3. The Languages Accepted by Turing
Page 174 and 175:
3. The Languages Accepted by Turing
Page 176 and 177:
4. The Halting Problem for Turing M
Page 178 and 179:
5. Nondeterministic Turing Machines
Page 180 and 181:
5. Nondeterministic Turing Machines
Page 182 and 183:
6. Variations on the Turing Machine
Page 184 and 185:
Page 186 and 187:
Page 188 and 189:
7Processes and Grammars1. Semi-Thue
Page 190 and 191:
2. Simulation of Nondeterministic T
Page 192 and 193:
Page 194 and 195:
Page 196 and 197:
3. Unsolvable Word Problems 177We w
Page 198 and 199:
3. Unsolvable Word Problems 179Proo
Page 200 and 201:
4. Post's Correspondence Problem 18
Page 202 and 203:
4. Post's Correspondence Problem183
Page 204 and 205:
4. Post's Correspondence Problem185
Page 206 and 207:
5. Grammars187Now, let L accept u E
Page 208 and 209:
5. Grammars 189We now are able to o
Page 210 and 211:
6. Some Unsolvable Problems Concern
Page 212 and 213:
7. Normal Processes 193to indicate
Page 214:
7. Normal Processes 195Lemma 5. Let
Page 217 and 218:
198 Chapter 8 Classifying Unsolvabl
Page 219 and 220:
Page 221 and 222:
Page 223 and 224:
Page 225 and 226:
Page 227 and 228:
Page 229 and 230:
Page 231 and 232:
Page 233 and 234:
Page 235 and 236:
Page 237 and 238:
Page 239 and 240:
Page 241 and 242:
Page 243 and 244:
Page 245 and 246:
Page 247 and 248:
Page 249 and 250:
Page 251 and 252:
Page 253 and 254:
Page 256 and 257:
9Regular Languages1. Finite Automat
Page 258 and 259:
1. Finite Automata 239is the initia
Page 260 and 261:
1. Finite Automata 241(a) A = {1};
Page 262 and 263:
2. Nondeterministic Finite Automata
Page 264 and 265:
2. Nondeterministic Finite Automata
Page 266 and 267:
3. Additional Examples 2472. For ea
Page 268 and 269:
4. Closure Properties 249aabFigure3
Page 270 and 271:
4. Closure Properties 251(That is,
Page 272 and 273:
5. Kleene's Theorem 253a 1 ••
Page 274 and 275:
5. Kleene's Theorem 255Chapter 4. I
Page 276 and 277:
5. Kleene's Theorem 257For each reg
Page 278 and 279:
5. Kleene's Theorem 259(Note that p
Page 280 and 281:
6. The Pumping Lemma and Its Applic
Page 282 and 283:
7. The Myhill- Nerode Theorem 2637.
Page 284 and 285:
7. The Myhill- Nerode Theorem 265wo
Page 286:
7. The Myhill- Nerode Theorem 26713
Page 289 and 290:
270 Chapter 10 Context-Free Languag
Page 291 and 292:
272 Chapter 1 0 Context-Free Langua
Page 293 and 294:
Page 295 and 296:
Page 297 and 298:
Page 299 and 300:
Page 301 and 302:
Page 303 and 304:
Page 305 and 306:
286Chapter 1 0 Context-Free Languag
Page 307 and 308:
Page 309 and 310:
Page 311 and 312:
Page 313 and 314:
294 Chapter 1 0 Context-Free lanQua
Page 315 and 316:
Page 317 and 318:
Page 319 and 320:
Page 321 and 322:
Page 323 and 324:
Page 325 and 326:
Page 327 and 328:
308Chapter 1 0 Context-Free Languag
Page 329 and 330:
Page 331 and 332:
Page 333 and 334:
Page 335 and 336:
Page 337 and 338:
Page 339 and 340:
Page 341 and 342:
Page 343 and 344:
Page 345 and 346:
Page 347 and 348:
328 Chapter 11 Context-Sensitive La
Page 349 and 350:
Page 351 and 352:
Page 353 and 354:
Page 355 and 356:
Page 357 and 358:
Page 359 and 360:
Page 361 and 362:
nlwlknlwl342 Chapter 11 Context-Sen
Page 363 and 364:
Page 366 and 367:
12Propositional Calculus1. Formulas
Page 368 and 369:
1. Formulas and Assignments 349Tabl
Page 370 and 371:
1. Formulas and Assignments351secon
Page 372 and 373:
3. Normal Forms 353Consider the exa
Page 374 and 375:
3. Normal Forms 355that there are t
Page 376 and 377:
3. Normal Forms 357Use of (II) agai
Page 378 and 379:
3. Normal Forms 359This problem has
Page 380 and 381:
4. The Davis- Putnam Rules 361We wi
Page 382 and 383:
4. The Davis- Putnam Rules363Succes
Page 384 and 385:
4. The Davis- Putnam Rules 365of th
Page 386 and 387:
6. Resolution 367Then it is very ea
Page 388 and 389:
6. Resolution 369j, k < i. Hence, b
Page 390 and 391:
7. The Compactness Theorem 371for n
Page 392:
7. The Compactness Theorem 373adjac
Page 395 and 396:
376 Chapter 13 Quantification Theor
Page 397 and 398:
Page 399 and 400:
Page 401 and 402:
Page 403 and 404:
Page 405 and 406:
Page 407 and 408:
Page 409 and 410:
Page 411 and 412:
Page 413 and 414:
Page 415 and 416:
Page 417 and 418:
Page 419 and 420:
Page 421 and 422:
Page 423 and 424:
Page 425 and 426:
Page 427 and 428:
Page 429 and 430:
Page 431 and 432:
Page 433 and 434:
Page 436:
Part 4Complexity
Page 439 and 440:
420 Chapter 14 Abstract Complexityi
Page 441 and 442:
422 Chapter 14 Abstract ComplexityO
Page 443 and 444:
424 Chapter 14 Abstract Complexity2
Page 445 and 446:
426 Chapter 14 Abstract ComplexityT
Page 447 and 448:
428 Chapter 14 Abstract Complexity2
Page 449 and 450:
430 Chapter 14 Abstract Complexityr
Page 451 and 452:
432 Chapter 14 Abstract ComplexityX
Page 453 and 454:
434 Chapter 14 Abstract ComplexityH
Page 455 and 456:
436Chapter 14 Abstract ComplexityV+
Page 457 and 458:
438 Chapter 14 Abstract ComplexityF
Page 459 and 460:
440 Chapter 15 Polynomial- Time Com
Page 461 and 462:
442 Chapter 15 Polynomial-Time Comp
Page 463 and 464:
Page 465 and 466:
Page 467 and 468:
Page 469 and 470:
Page 471 and 472:
Page 473 and 474:
Page 475 and 476:
Page 477 and 478:
Page 479 and 480:
Page 481 and 482:
Page 484:
Part 5Semantics
Page 487 and 488:
468 Chapter 16 Approximation Orderi
Page 489 and 490:
Page 491 and 492:
Page 493 and 494:
Page 495 and 496:
Page 497 and 498:
Page 499 and 500:
Page 501 and 502:
Page 503 and 504:
Page 505 and 506:
Page 507 and 508:
Page 509 and 510:
Page 511 and 512:
Page 513 and 514:
Page 515 and 516:
Page 517 and 518:
Page 519 and 520:
Page 521 and 522:
Page 524 and 525:
17Denotational Semanticsof Recursio
Page 526 and 527:
1. Syntax 507We extend rand p to VA
Page 528 and 529:
1. Syntax 509will remain fixed thro
Page 530 and 531:
2. Semantics of Terms 511(c)Let (W,
Page 532 and 533:
2. Semantics of Terms 5135. For all
Page 534 and 535:
2. Semantics of Terms 515based on :
Page 536 and 537:
2. Semantics of Terms517write Or-;:
Page 538 and 539:
2. Semantics of Terms 519Exercises1
Page 540 and 541:
3. Solutions to W-Programs 521When
Page 542 and 543:
3. Solutions to W-Programs 523Theor
Page 544 and 545:
3. Solutions to W-Programs 525so JL
Page 546 and 547:
3. Solutions to W-Programs 527If i
Page 548 and 549:
3. Solutions to W-Programs 5299. Le
Page 550 and 551:
4. Denotational Semantics of W-Prog
Page 552 and 553:
4. Denotatlonal Semantics of W-Prog
Page 554 and 555:
Page 556 and 557:
Page 558 and 559:
5. Simple Data Structure Systems 53
Page 560 and 561:
Page 562 and 563:
Page 564 and 565:
6. lnfinltary Data Structure System
Page 566 and 567:
6. lnfinitary Data Structure System
Page 568 and 569:
Page 570 and 571:
Page 572 and 573:
Page 574 and 575:
Page 576 and 577:
18Operational Semanticsof Recursion
Page 578 and 579:
1. Operational Semantics for Simple
Page 580 and 581:
Page 582 and 583:
Page 584 and 585:
Page 586 and 587:
Page 588 and 589:
Page 590 and 591:
Page 592 and 593:
Page 594 and 595:
2. Computable Functions5757. Let P
Page 596 and 597:
2. Computable Functions 577Then for
Page 598 and 599:
2. Computable Functions579Let (x 1
Page 600 and 601:
2. Computable Functions 581It is cl
Page 602 and 603:
2. Computable Functions 5833. Let P
Page 604 and 605:
3. lnflnltary Data Structure System
Page 606 and 607:
Page 608 and 609:
Page 610 and 611:
3. lnflnltary Data Structure System
Page 612 and 613:
Suggestions for Further ReadingC. L
Page 614 and 615:
Notation IndexE 1 (3t), (Vt) 70 1
Page 616 and 617:
Notation Index 597p 444 F(XH ... ,X
Page 618 and 619:
IndexAlgorithms, 3, 68, 79-80, 95,
Page 620 and 621:
Indexnonregular, 270and pushdown au
Page 622 and 623:
IndexHorn clauses, 403Horn programs
Page 624 and 625:
IndexpP,444-446, 448,449,456,461Pai
Page 626 and 627:
IndexRogers, Hartley, 594Rooted sen
Page 628:
Indexbound, 376-377free, 376-377fun
show all

Computability complexity and Languages- Fundamentals of Theoretical Computer Science

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?