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Jones N.D. — Computability and complexity from a programming perspective
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Название: Computability and complexity from a programming perspective
Автор: Jones N.D.
Аннотация: "Neil Jones is one of the precious few computer scientists with great expertise and leadership roles in both formal methods and complexity. This makes his book especially valuable." — Yuri Gurevich, Professor of Computer Science, University of Michigan
Computability and complexity theory should be of central concern to practitioners as well as theorists. Unfortunately, however, the field is known for its impenetrability. Neil Jones's goal as an educator and author is to build a bridge between computability and complexity theory and other areas of computer science, especially programming. In a shift away from the Turing machine- and G?del number-oriented classical approaches, Jones uses concepts familiar from programming languages to make computability and complexity more accessible to computer scientists and more applicable to practical programming problems. According to Jones, the fields of computability and complexity theory, as well as programming languages and semantics, have a great deal to offer each other. Computability and complexity theory have a breadth, depth, and generality not often seen in programming languages. The programming language community, meanwhile, has a firm grasp of algorithm design, presentation, and implementation. In addition, programming languages sometimes provide computational models that are more realistic in certain crucial aspects than traditional models. New results in the book include a proof that constant time factors do matter for its programming-oriented model of computation. (In contrast, Turing machines have a counterintuitive "constant speedup" property: that almost any program can be made to run faster, by any amount. Its proof involves techniques irrelevant to practice.) Further results include simple characterizations in programming terms of the central complexity classes PTIME and LOGSPACE, and a new approach to complete problems for NLOGSPACE, PTIME, NPTIME, and PSPACE, uniformly based on Boolean programs. Foundations of Computing series
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Рубрика: Computer science /
Статус предметного указателя: Готов указатель с номерами страниц
ed2k: ed2k stats
Год издания: 1997
Количество страниц: 457
Добавлена в каталог: 01.12.2013
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Предметный указатель
Hilbert, D. 167
Horn clause 391
i 72
Implements 52
Implication 192
Indirect fetch 119
Indirect store 119
Induction 439
Induction, complete 439
Induction, course-of-values 439
Induction, hypothesis 439
Inference relation 195
Inference rule 189
Inference system 188 195
Infinite sequence 424
Initial store 264
Intensional 226 240
Interpreter 54
Interpreter, efficient 286
Interpreter, overhead 90
Interpreting function 54
Invariance 241
Invariance Thesis 21
Isomorphism theorem 231
judgment 189
LAMBDA 140
Lambda calculus 8
Lambda notation 427
Language, accepted by DFA 437
Language, accepted by NFA 437
Language, equivalent 48
Language, functional 137
Language, imperative 137
Language, implementation 53 58
Language, simulating one by another 48
Language, source 53 57
Language, target 57
Left-most multi-step derivation relation 433
Left-most one-step derivation relation 433
Length (of a list) 33
Length of a read-only TMro state 317
Length of a state 316
Linear time 276 291
Linearly equivalent 252
LINTIME 272 276
LIST 33 35
List representation 33
Literal 419
Logarithmic cost 255 257
LOGSPACB 319 322 346 351
LOGSPACE functions 325
lookup 55
Markov algorithms 8
Match 40 57
MCV 390
Minimization 208
Model-independent 225
Monotone circuit 383
Multi-step derivation relation 433
Multi-step rewrite relation 153
n-tuples 422
Natural numbers 421
Natural semantics 188
Negation 32 192 419
NFA 436
NLINTIME 378
NLOGSPACE 333 345 346
nodes 430
Non-deterministic finite automaton 436
Nondeterminism 243 331
Nonterminals 432
Nonuniform complexity xv
Normal form 142
Normal Form Theorem 210
Normalizations 335
NPSPACE 333 345 346
NPTIME 243 333 346
Numerals 34
o-notation 429
Omega-notation 429
One-step derivation relation 433
One-step rewrite relation 153
Operational semantics 188
Optimality of a specializer 103
Ordered pair 422
Overhead factor 252
Pairing 53
Pairing decomposition 442
Parallelism xv
Parallelism, PTIME 395
Partial evaluation 65 77 96
Partial evaluation, off-line 106
Partial evaluation, techniques 104
Partial recursive 205
Partial recursive functions 24
Pascal-like implementation of GOTO 266
Path finding 332
Pattern 40
PCP 156
Polynomial-time 274
Polynomially equivalent 252
Post's correspondence problem 156
Predecessor 34
Predicate 192 195
Prefix 431
Primitive recursion 206
Problem 3
Problem, ambiguity 161 434
Problem, complete for NLINTIME 378
Problem, complete for NLOGSPACE 376
Problem, complete for RE 375
Problem, completeness 161 434
Problem, membership 434
Problem, natural unsolvable 151
Problem, non-emptiness for 434
Problem, representation 271
Problem, representation of 368
Problem, undeddable 154
Production 153
Program padding 233
Program point specialization 105
Program property 79
Program property, extensional 79
Program property, intensional 79
Program property, nontrivial 79
Program spedalizer 58 227
Program spedalizer, optimal 103
Program, boolean 407
Program, computes a function 38
Program, function computed by 38
Program, looping 38
Program, self-reproducing 222
Program, stack 288
Program, terminating 38
Program, time-bounded 271
Program, timed universal 288
Program-dependent 253 256
Program-independent 253
Programming language 47
Programs, cons-free 349 355
Proof tree 197
Propositional formulas 419
Provability 202
PSPACE 319 322 345 346 407
PTIME 244 272 275 322 345 346 355
Pushdown automaton 359
Quadruples 422
Quantified boolean algebra 409
r.e. see "Recursively enumerable"
RAM 111
Random access machine 8 118
read-only 315
Readin 113
Readout 113
Real numbers xv 421
Real numbers, positive 421
Recursion theorem 220 229
RECURSIVE 86
Recursive extension 355
Recursive function 8 205
Recursive function theory 205
Recursively enumerable 86 195 197 202
Redex 142
Reducing SAT to CLIQUE 370
Reduction 152 365 366
Reduction function 368
Reflexive extension 222
REGALL 434
REGAMB 434
Regular expression 435
Regular expression, set generated by 435
Regular expression, totality 412
Regular grammar see "Grammar"
Representable predicate 200
Resource bound 271 332
Resources 242
Restriction to one operator 60
Restriction to one variable 61
reverse 30 432
Rewrite rule 153
Rice's theorem 78
Robust 147 274 276 322
Robustness 241 271
Robustness, computability 127
Rogers, H 226 231
Rooted DSG 262
Running time 275
Running time function 90
Running time, WHILE program 254
Russell's paradox 15
s-m-n function property 227
SAT 367 370 397
Satisfiable 443
Second component 422
Self-interpreter 72 227
Self-reproducing program 222
Semantic function 47 90
Semi-decidable 76
Semi-Thue 153
Set 421
Set, contained in 421
Set, countable 14
Set, deciding membership of 10
Set, difference 422
Set, Diophantine 169
Set, element of 421
Set, empty 421
Set, equality 421
Set, exponential Diophantine 169
Set, intersection 422
Set, member of 421
Set, union 422
Simulation with data change 129
Simulation, invariant 135
Single-assignment 383
Size (of a tree) 29
Slowdown 252
Software viewpoint 9
solvable 4
Source program 50
Space usage 332
SPACE(f) 319
Space-bounded programs 319
Space-constructible 328
Specialization 205
Specializing function 59
Spedalizer 59
Spedalizer properties, computational completeness 102
Spedalizer properties, optimality 103
Spedalizer properties, totality 102
Speedup 252
SRAM 119
Stack programs 288 359
Start state 436 437
Start symbol 432
State 112 114 264
State transition graph 337 343
State, terminal 112
States (of an DFA) 437
States (of an NFA) 436
Stochastic algorithms xv
Storage Modification Machine 255
STORE 36 37 112 114 137 189 264
Store, initial 37
String 431
String matching 359 360
String rewriting 153
String, accepted by DFA 437
String, accepted by NFA 437
String, bit 250
String, concatenation 431
String, configuration 155
String, empty 431
Strongly linearly equivalent 253
Structural operational semantics 188
Sublinear 315
Subset 421
Substring 431
Successor 34
Successor random access machine 119
Suffix 431
Superlinear time 292
Symbolic computation 105
symbols 431
Tape alphabet 115
Terminals 432
Theorem 196
Theorem, normal form 129
Theta-notation 429
TI-diagrams 51
Time constructible 293 297
Time usage 332
TIME(f) 272
Time, linear 276
Time, superlinear 292
Timed programming language 89
Timed universal program 288
TM 111
TMro 316
Totality of a spedalizer 102
Tractable 244
Transition function 436 437
Treeless transformer 353
Triples 422
TRUE 32 419
Truth 202
Truth assignment 420
Truth table 420
Truth values 419
Tupling function 225
Turing completeness 227
Turing machine 5 8 115 316
Turing machine, configuration 122
Turing machine, deterministic 121
Turing machine, enumeration 225
Turing machine, program 225
Uncomputable function see "Undecidable"
Uncomputable functions 16
Undecidable 78 154
Undirected graph 431
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