Knowledge

Nonelementary problem

Source 📝

294:
Pratt-Hartmann, Ian; Szwast, Wieslaw; Tendera, Lidia (2016), "Quine's fluted fragment is non-elementary", in Talbot, Jean-Marc; Regnier, Laurent (eds.),
253:
Automated Deduction — CADE-13: 13th International Conference on Automated Deduction New Brunswick, NJ, USA, July 30 – August 3, 1996, Proceedings
504: 389: 528: 36: 323: 440: 278: 156: 497: 296:
25th EACSL Annual Conference on Computer Science Logic, CSL 2016, August 29 - September 1, 2016, Marseille, France
17: 131:
Proceedings of the Seventeenth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems (PODS '98)
490: 470: 523: 46: 261: 139: 298:, LIPIcs, vol. 62, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, pp. 39:1–39:21, 478: 256: 134: 86: 77: 237: 96: 82: 184: 8: 251:
Vorobyov, Sergei (1996), "An improved lower bound for the elementary theories of trees",
50: 418: 365: 215: 162: 104: 90: 436: 336: 274: 152: 71: 54: 166: 428: 340: 332: 299: 266: 225: 180: 144: 42: 229: 432: 394: 318: 255:, Lecture Notes in Computer Science, vol. 1104, Springer, pp. 275–287, 233: 126: 474: 410: 304: 67: 517: 364:. 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS). 270: 203: 31:
Examples of nonelementary problems that are nevertheless decidable include:
61: 148: 415:
2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)
345: 129:(1998), "Complexity of Nonrecursive Logic Programs with Complex Values", 25: 220: 100: 411:"The Reachability Problem for Petri Nets is Not Primitive Recursive" 423: 370: 390:"An Easy-Sounding Problem Yields Numbers Too Big for Our Universe" 186:
The Complexity of Decision Problems in Automata Theory and Logic
362:
Reachability in Vector Addition Systems is Ackermann-complete
321:(1979), "The typed λ-calculus is not elementary recursive", 293: 192:, Ph.D. dissertation, Massachusetts Institute of Technology 28:. As a class it is sometimes denoted as NONELEMENTARY. 359: 37:
regular expression equivalence with complementation
206:(2006), "Logics for unranked trees: an overview", 360:Czerwiński, Wojciech; Orlikowski, Łukasz (2021). 76:deciding β-convertibility of two closed terms in 515: 124: 24:is a problem that is not a member of the class 498: 133:, New York, NY, USA: ACM, pp. 244–253, 505: 491: 179: 422: 369: 344: 303: 260: 219: 138: 387: 250: 317: 516: 408: 202: 456: 383: 381: 208:Logical Methods in Computer Science 13: 529:Theoretical computer science stubs 14: 540: 388:Brubaker, Ben (4 December 2023). 378: 409:Leroux, Jerome (February 2022). 18:computational complexity theory 402: 353: 311: 287: 244: 196: 173: 118: 1: 111: 477:. You can help Knowledge by 471:theoretical computer science 433:10.1109/FOCS52979.2021.00121 417:. IEEE. pp. 1241–1252. 337:10.1016/0304-3975(79)90007-0 324:Theoretical Computer Science 7: 10: 545: 455: 305:10.4230/LIPIcs.CSL.2016.39 47:monadic second-order logic 60:the decision problem for 271:10.1007/3-540-61511-3_91 230:10.2168/LMCS-2(3:2)2006 87:vector addition systems 473:–related article is a 70:'s fluted fragment of 149:10.1145/275487.275515 78:typed lambda calculus 22:nonelementary problem 181:Stockmeyer, Larry J. 524:Complexity classes 125:Vorobyov, Sergei; 66:satisfiability of 486: 485: 442:978-1-6654-2055-6 280:978-3-540-61511-8 158:978-0-89791-996-8 72:first-order logic 536: 507: 500: 493: 462:P ≟ NP 457: 447: 446: 426: 406: 400: 399: 385: 376: 375: 373: 357: 351: 349: 348: 319:Statman, Richard 315: 309: 308: 307: 291: 285: 283: 264: 248: 242: 240: 223: 200: 194: 193: 191: 177: 171: 169: 142: 127:Voronkov, Andrei 122: 43:decision problem 544: 543: 539: 538: 537: 535: 534: 533: 514: 513: 512: 511: 464: 453: 451: 450: 443: 407: 403: 395:Quanta Magazine 386: 379: 358: 354: 316: 312: 292: 288: 281: 249: 245: 201: 197: 189: 178: 174: 159: 123: 119: 114: 35:the problem of 12: 11: 5: 542: 532: 531: 526: 510: 509: 502: 495: 487: 484: 483: 466: 460: 449: 448: 441: 401: 377: 352: 310: 286: 279: 262:10.1.1.39.1499 243: 214:(3): 3:2, 31, 204:Libkin, Leonid 195: 172: 157: 140:10.1.1.39.8822 116: 115: 113: 110: 109: 108: 94: 80: 74: 68:W. V. O. Quine 64: 58: 39: 9: 6: 4: 3: 2: 541: 530: 527: 525: 522: 521: 519: 508: 503: 501: 496: 494: 489: 488: 482: 480: 476: 472: 467: 463: 459: 458: 454: 444: 438: 434: 430: 425: 420: 416: 412: 405: 397: 396: 391: 384: 382: 372: 367: 363: 356: 347: 346:2027.42/23535 342: 338: 334: 330: 326: 325: 320: 314: 306: 301: 297: 290: 282: 276: 272: 268: 263: 258: 254: 247: 239: 235: 231: 227: 222: 221:cs.LO/0606062 217: 213: 209: 205: 199: 188: 187: 182: 176: 168: 164: 160: 154: 150: 146: 141: 136: 132: 128: 121: 117: 106: 102: 98: 95: 92: 88: 84: 81: 79: 75: 73: 69: 65: 63: 62:term algebras 59: 56: 52: 48: 44: 40: 38: 34: 33: 32: 29: 27: 23: 19: 479:expanding it 468: 461: 452: 414: 404: 393: 361: 355: 328: 322: 313: 295: 289: 252: 246: 211: 207: 198: 185: 175: 130: 120: 97:reachability 83:reachability 30: 21: 15: 518:Categories 424:2104.12695 371:2104.13866 112:References 107:-complete. 101:Petri nets 93:-complete. 26:ELEMENTARY 331:: 73–81, 257:CiteSeerX 135:CiteSeerX 105:Ackermann 91:Ackermann 183:(1974), 167:15631793 103:; it is 89:; it is 238:2295773 465:  439:  277:  259:  236:  165:  155:  137:  469:This 419:arXiv 366:arXiv 216:arXiv 190:(PDF) 163:S2CID 53:(see 51:trees 49:over 20:, a 475:stub 437:ISBN 275:ISBN 153:ISBN 45:for 41:the 429:doi 341:hdl 333:doi 300:doi 267:doi 226:doi 145:doi 99:in 85:in 55:S2S 16:In 520:: 435:. 427:. 413:. 392:. 380:^ 339:, 327:, 273:, 265:, 234:MR 232:, 224:, 210:, 161:, 151:, 143:, 506:e 499:t 492:v 481:. 445:. 431:: 421:: 398:. 374:. 368:: 350:. 343:: 335:: 329:9 302:: 284:. 269:: 241:. 228:: 218:: 212:2 170:. 147:: 57:)

Index

computational complexity theory
ELEMENTARY
regular expression equivalence with complementation
decision problem
monadic second-order logic
trees
S2S
term algebras
W. V. O. Quine
first-order logic
typed lambda calculus
reachability
vector addition systems
Ackermann
reachability
Petri nets
Ackermann
Voronkov, Andrei
CiteSeerX
10.1.1.39.8822
doi
10.1145/275487.275515
ISBN
978-0-89791-996-8
S2CID
15631793
Stockmeyer, Larry J.
The Complexity of Decision Problems in Automata Theory and Logic
Libkin, Leonid
arXiv

Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.