Knowledge

R (complexity)

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592: 104: 153: 102:, (1989), "On a theory of computation and complexity over the real numbers: NP-completeness, recursive functions and universal machines", 621: 585: 515: 146: 17: 616: 578: 558: 611: 139: 531: 338: 76:
and also a co-recogniser by simply interleaving them until one obtains a result, the class is equal to
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Since we can decide any problem for which there exists a
67: 59:a total function is computable if and only if its 603: 52:a decision problem is in R if and only if its 586: 147: 105:Bulletin of the American Mathematical Society 593: 579: 154: 140: 39: 44:R is equivalent to the set of all total 604: 161: 135: 544: 36:(also called decidable languages). 13: 622:Theoretical computer science stubs 14: 633: 516:Probabilistically checkable proof 116: 68:Relationship with other classes 18:computational complexity theory 1: 89: 565:. You can help Knowledge by 559:theoretical computer science 7: 10: 638: 543: 532:List of complexity classes 32:, which is the set of all 529: 488: 452: 396: 289: 169: 521:Interactive proof system 40:Equivalent formulations 561:–related article is a 475:Arithmetical hierarchy 470:Grzegorczyk hierarchy 465:Exponential hierarchy 397:Considered infeasible 617:Computability theory 460:Polynomial hierarchy 290:Suspected infeasible 46:computable functions 489:Families of classes 170:Considered feasible 48:in the sense that: 34:recursive languages 612:Complexity classes 163:Complexity classes 54:indicator function 574: 573: 538: 537: 480:Boolean hierarchy 453:Class hierarchies 98:, Mike Shub, and 26:decision problems 629: 595: 588: 581: 550:P ≟ NP 545: 156: 149: 142: 133: 132: 24:is the class of 637: 636: 632: 631: 630: 628: 627: 626: 602: 601: 600: 599: 552: 541: 539: 534: 525: 484: 448: 392: 386:PSPACE-complete 285: 165: 160: 119: 92: 70: 42: 12: 11: 5: 635: 625: 624: 619: 614: 598: 597: 590: 583: 575: 572: 571: 554: 548: 536: 535: 530: 527: 526: 524: 523: 518: 513: 508: 503: 498: 492: 490: 486: 485: 483: 482: 477: 472: 467: 462: 456: 454: 450: 449: 447: 446: 441: 436: 431: 426: 421: 416: 411: 406: 400: 398: 394: 393: 391: 390: 389: 388: 378: 373: 372: 371: 361: 356: 351: 346: 341: 336: 331: 326: 325: 324: 322:co-NP-complete 319: 314: 309: 299: 293: 291: 287: 286: 284: 283: 278: 273: 268: 263: 258: 253: 252: 251: 241: 236: 231: 226: 225: 224: 214: 209: 204: 199: 194: 189: 184: 179: 173: 171: 167: 166: 159: 158: 151: 144: 136: 123:Complexity Zoo 118: 117:External links 115: 114: 113: 108:, New Series, 91: 88: 69: 66: 65: 64: 57: 56:is computable, 41: 38: 30:Turing machine 28:solvable by a 9: 6: 4: 3: 2: 634: 623: 620: 618: 615: 613: 610: 609: 607: 596: 591: 589: 584: 582: 577: 576: 570: 568: 564: 560: 555: 551: 547: 546: 542: 533: 528: 522: 519: 517: 514: 512: 509: 507: 504: 502: 499: 497: 494: 493: 491: 487: 481: 478: 476: 473: 471: 468: 466: 463: 461: 458: 457: 455: 451: 445: 442: 440: 437: 435: 432: 430: 427: 425: 422: 420: 417: 415: 412: 410: 407: 405: 402: 401: 399: 395: 387: 384: 383: 382: 379: 377: 374: 370: 367: 366: 365: 362: 360: 357: 355: 352: 350: 347: 345: 342: 340: 337: 335: 332: 330: 327: 323: 320: 318: 315: 313: 310: 308: 305: 304: 303: 300: 298: 295: 294: 292: 288: 282: 279: 277: 274: 272: 269: 267: 264: 262: 259: 257: 254: 250: 247: 246: 245: 242: 240: 237: 235: 232: 230: 227: 223: 220: 219: 218: 215: 213: 210: 208: 205: 203: 200: 198: 195: 193: 190: 188: 185: 183: 180: 178: 175: 174: 172: 168: 164: 157: 152: 150: 145: 143: 138: 137: 134: 130: 129: 125: 124: 111: 107: 106: 101: 97: 94: 93: 87: 85: 81: 80: 75: 62: 58: 55: 51: 50: 49: 47: 37: 35: 31: 27: 23: 19: 567:expanding it 556: 549: 540: 433: 121: 120: 109: 103: 96:Blum, Lenore 83: 78: 71: 43: 21: 15: 369:#P-complete 307:NP-complete 222:NL-complete 100:Steve Smale 606:Categories 424:ELEMENTARY 249:P-complete 112:(1): 1-46. 90:References 74:recogniser 419:2-EXPTIME 414:EXPSPACE 409:NEXPTIME 177:DLOGTIME 63:is in R. 404:EXPTIME 312:NP-hard 128:Class R 553:  511:NSPACE 506:DSPACE 381:PSPACE 557:This 501:NTIME 496:DTIME 317:co-NP 84:co-RE 61:graph 563:stub 329:TFNP 444:ALL 344:QMA 334:FNP 276:APX 271:BQP 266:BPP 256:ZPP 187:ACC 16:In 608:: 439:RE 429:PR 376:IP 364:#P 359:PP 354:⊕P 349:PH 339:AM 302:NP 297:UP 281:FP 261:RP 239:CC 234:SC 229:NC 217:NL 212:FL 207:RL 202:SL 192:TC 182:AC 126:: 110:21 86:. 82:∩ 79:RE 20:, 594:e 587:t 580:v 569:. 434:R 244:P 197:L 155:e 148:t 141:v 22:R

Index

computational complexity theory
decision problems
Turing machine
recursive languages
computable functions
indicator function
graph
recogniser
RE
Blum, Lenore
Steve Smale
Bulletin of the American Mathematical Society
Complexity Zoo
Class R
v
t
e
Complexity classes
DLOGTIME
AC
ACC
TC
L
SL
RL
FL
NL
NL-complete
NC
SC

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