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polyL

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256:
under logarithmic space many-one reductions has led Ferrarotti et al. to define a different notion of completeness for this class, involving transformations from parameterized problems to polylog-space machines that solve the problems for specific parameter values.
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Ferrarotti, Flavio; González, Senén; Schewe, Klaus-Dieter; Torres, José Maria Turull (2022), "Uniform polylogarithmic space completeness",
387: 286: 20: 380: 360: 36: 418: 154: 274: 90: 146: 282: 143: 330: 139: 40: 32: 28: 44: 364: 301: 80: 74: 66: 407: 306: 335: 53: 126:, or if neither is contained in the other. One proof that 368: 47:function in the size of the input. In other words, 249:) and hence violates the space hierarchy theorem. 94:. However, the only proven relationship between 157:. The space hierarchy theorem guarantees that 388: 189:) for some integer k > 0. Suppose problem 8: 316: 314: 395: 381: 334: 213:is complete implies the following O(log 266: 16:Complexity class of decision problems 7: 348: 346: 414:Theoretical computer science stubs 252:The lack of complete problems for 229:in logarithmic space, then decide 14: 177:had a complete problem, call it 173:) for all integers d > 0. If 281:, Addison-Wesley, p. 405, 21:computational complexity theory 1: 323:Frontiers in Computer Science 367:. You can help Knowledge by 361:theoretical computer science 181:, it would be an element of 65:denotes the input size, and 37:deterministic Turing machine 237:) space. This implies that 435: 345: 275:Papadimitriou, Christos H. 336:10.3389/FCOMP.2022.845990 279:Computational Complexity 69:(1) denotes a constant. 35:that can be solved on a 209:). The assumption that 155:space hierarchy theorem 363:–related article is a 217:) space algorithm for 39:by an algorithm whose 153:does not due to the 147:many-one reductions 110:; it is unknown if 419:Complexity classes 376: 375: 241:is an element of 193:is an element of 144:logarithmic space 33:decision problems 426: 397: 390: 383: 352:P ≟ NP 347: 340: 339: 338: 318: 309: 298: 292: 291: 271: 140:complete problem 43:is bounded by a 41:space complexity 29:complexity class 434: 433: 429: 428: 427: 425: 424: 423: 404: 403: 402: 401: 354: 344: 343: 320: 319: 312: 299: 295: 289: 273: 272: 268: 263: 45:polylogarithmic 17: 12: 11: 5: 432: 430: 422: 421: 416: 406: 405: 400: 399: 392: 385: 377: 374: 373: 356: 350: 342: 341: 310: 302:Complexity Zoo 293: 287: 265: 264: 262: 259: 15: 13: 10: 9: 6: 4: 3: 2: 431: 420: 417: 415: 412: 411: 409: 398: 393: 391: 386: 384: 379: 378: 372: 370: 366: 362: 357: 353: 349: 337: 332: 328: 324: 317: 315: 311: 308: 304: 303: 297: 294: 290: 288:9780201530827 284: 280: 276: 270: 267: 260: 258: 255: 250: 248: 244: 240: 236: 232: 228: 224: 220: 216: 212: 208: 204: 200: 196: 192: 188: 184: 180: 176: 172: 168: 164: 160: 156: 152: 148: 145: 141: 137: 133: 129: 125: 121: 117: 113: 109: 105: 101: 97: 93: 92: 87: 83: 82: 77: 76: 70: 68: 64: 60: 56: 55: 51: =  50: 46: 42: 38: 34: 30: 26: 22: 369:expanding it 358: 351: 326: 322: 300: 296: 278: 269: 253: 251: 246: 242: 238: 234: 230: 226: 222: 218: 214: 210: 206: 202: 198: 194: 190: 186: 182: 178: 174: 170: 166: 162: 158: 150: 135: 131: 127: 123: 119: 115: 111: 107: 103: 99: 95: 89: 85: 79: 73: 71: 62: 58: 52: 48: 24: 18: 57:((log  408:Categories 329:: 845990, 261:References 61:)), where 233:in O(log 221:: reduce 277:(1994), 134:is that 102:is that 72:Just as 27:is the 355:  285:  243:DSPACE 203:DSPACE 195:DSPACE 183:DSPACE 167:DSPACE 159:DSPACE 142:under 138:has a 54:DSPACE 359:This 307:polyL 254:polyL 245:(log 205:(log 197:(log 185:(log 175:polyL 169:(log 161:(log 151:polyL 128:polyL 124:polyL 118:, if 112:polyL 104:polyL 96:polyL 86:polyL 49:polyL 25:polyL 365:stub 283:ISBN 201:) \ 165:) ⊊ 149:but 98:and 331:doi 225:to 31:of 19:In 410:: 325:, 313:^ 305:: 130:≠ 122:⊊ 114:⊊ 106:≠ 91:QP 88:⊆ 84:, 78:⊆ 23:, 396:e 389:t 382:v 371:. 333:: 327:4 247:n 239:B 235:n 231:A 227:A 223:B 219:B 215:n 211:A 207:n 199:n 191:B 187:n 179:A 171:n 163:n 136:P 132:P 120:P 116:P 108:P 100:P 81:P 75:L 67:O 63:n 59:n

Index

computational complexity theory
complexity class
decision problems
deterministic Turing machine
space complexity
polylogarithmic
DSPACE
O
L
P
QP
complete problem
logarithmic space
many-one reductions
space hierarchy theorem
Papadimitriou, Christos H.
ISBN
9780201530827
Complexity Zoo
polyL


doi
10.3389/FCOMP.2022.845990
theoretical computer science
stub
expanding it
v
t
e

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