Index

| · |, (see cardinality of set; length of string)
×, (see Cartesian product)
é·ù (ceiling function), 301
Ĝ, (see empty set)
e, (see empty string)
˘ / $, (see endmarker)
S*, S+, 3
acceptance problem, 36
accepting computation / configuration / state, (see computation / configuration / state, accepting)
acyclic graph, 301
Adleman, L., 298, 302
Aho, A., 89, 267, 302
algorithm, 33
Allender, E., 298, 302
alphabet, 2 - 4
	binary, 2
	unary, 2
alphabetically
	bigger / smaller, 3
	ordered, 4
ambiguity problem, 36, 37, 197, 198
AND gate, 275
assertion, (see predicate)
assignment instruction, (see deterministic assignment instruction; nondeterministic assignment instruction; random assignment instruction)
auxiliary work-tape, 145
	alphabet / symbol, 146
	head, 145
bandwidth problem, 243
Bar-Hillel, Y., 90, 143, 198, 302
Batcher, K., 297, 302
Beauquier, J., 90
binary, (see alphabet / representation / string, binary)
Bird, M., 143, 302
Boolean
	circuit, (see circuit)
	expression, 215
Borodin, A., 298, 302
bounded-error, 258 - 259
BPP, 262ff.
Braffort, P., 305
Büchi, J., 89, 302
canonically
	bigger / smaller, 4
	ordered, 4
cardinality of set, 299
Cartesian product, 300
cascade composition, 89
Chandra, A., 298, 302
character, (see symbol)
Chomsky, N., 47, 90, 143, 197, 198, 302, 303
Church, A., 47, 197, 303
Church's thesis, 156
circuit, 275
	valued problem (CVP), 246, 247
clique problem, 224, 246
closure
	operation, the, (see Kleene closure)
	properties, 79 - 81, 89, 130 - 136, 142, 143, 193, 233 - 237, 241, 242, 246, 267
	under an operation, 79
Cobham, A., 246, 303
COMMON PRAM, (see parallel random access machine, COMMON)
complementation, 6, 7, 80 - 81, 130, 133, 143, 193, 233, 236, 242, 246, 300
complete / hard problem, 213, (see also P -complete/ -hard problem)
complexity
	depth, 270ff., 273ff., 277
	expected time, 249, 262
	size, 270, 273, 277
	space / time, 203 - 206, 262, 273
composition, 7, 89, 142, 143, 221, 245
computable function, 35
computation, 20, 58 - 60, 102 - 104, 153
	accepting / nonaccepting / rejecting, 20, 58, 102, 152, 258
	depth, 270, 273
	deterministic / nondeterministic, 21
	halting, 19, 21, 59
	probabilistic, 249, 258
concatenation, 3
conditional accept / if instruction, 17, 19, 20
configuration, 29, 55 - 56, 67, 110, 148
	accepting / initial, 30, 56, 67, 99, 148
configurations tree, 227, 236
conjunctive normal form, 220
connection language, 297
Constable, R., 246, 304
constant node, 275
content of pushdown store, 100
context-free grammar / language, 111ff., 187, 198, 238, 247
context-sensitive grammar / language, 47, 186 - 187, 198
Cook, S., 246, 298, 303
countable set, 301
countably infinite set, 173, 301
CREW PRAM, (see parallel random access machine, CREW)
cross product, 6
cycle in graph, 301
Danthine, A., 89, 303
decidability / partial decidability / undecidability, 32 - 35, 45 - 46, 47, 50, 82 - 84, 90, 136 - 138, 142 - 143, 173 - 179, 186, 188, 192ff., 195ff., 278, 289
decision problem, 32
defined value of function, 300
DeLeeuw, K., 268, 303
DeMorgan's law, 80
depth
	of circuit, 277ff.
	complexity, (see complexity, depth)
	of computation, (see computation, depth)
derivation, 10 - 12
	graph / tree, 12
	leftmost, 12, 114
deterministic
	assignment instruction, 17, 19
	computation, (see computation, deterministic)
	looping instruction, 17, 19
	program, 18 - 20
	transducer / automaton / machine, 57, 66, 101, 110, 152
diagonalization, 173, 195, 209, 289
difference, 6, 300
Diophantine polynomial / equation, 46, 50, 89, 244
directed graph, 301
disjoint sets, 300
DLOG, 205, 229
domain of
	function / relation, 300
	problem, 31
	variables of program, 16
DSPACE, 205, 225, 229, 236, 244, 245, 297
DTIME, 205, 208, 227, 236, 242, 243
DTIME_F, 282
e-free finite-state automaton, 66
e transition rule, 66
edge of graph, 301
Edmonds, J., 246, 303
Ehrenfeucht, A., 90, 303
emptiness / nonemptiness problem, 36, 37, 45, 50, 82 - 83, 90, 136, 137, 143, 196, 238, 245, 246, 247
empty
	pushdown store, 100
	set, 299
	string, 2
	-word membership problem, 34, 35, 196
encoding, (see representation)
endmarker, left / right, 147
eof -- end of input file, (see conditional accept instruction)
equivalence / inequivalence problem, 36, 37, 45, 46, 47, 82, 84, 90, 136 - 137, 143, 190, 196, 198, 232, 246
error-free probabilistic program, 248 - 251
error probability, 258 - 259
Evey, J., 143, 197, 303
execution sequence, 18 - 25
expected time complexity, (see complexity, expected time)
EXPTIME, 205, 213, 225, 229
family of circuits, 277ff.
final configuration / state, (see configuration / state, accepting)
finite
	-domain / -memory program, 48ff.
	-state control, 55, 95, 145
	-state transducer / automaton, 53 - 65, 130, 136, 142, 143, 190, 198, 232, 246
Floyd, R., 47, 303
FNC, 289
formal language, 7
Fortune, S., 298, 303
Freivalds, R., 268, 303
function, 300
	computed by, 258, 259, 275, 277, (see also relation computed by)
Garey, M., 247, 303
gate, 275
gcd, 301
Gill, J., 267, 268, 303
Goldschlager, L., 298, 304
grammar, 8ff., 11, 14 - 15
graph, (see directed graph)
graph accessibility problem, 243
Greibach, S., 143, 304
Griffiths, T., 198, 304
Grolmusz, V., 298, 304
Gurari, E., 143, 304
halting
	computation, (see computation, halting)
	on input, 60
	problem, 36, 82, 83, 138, 177, (see also uniform halting problem)
hard problem, (see complete problem)
Harrison, M., 47, 304
Hartmanis, J., 246, 304, 307
Hilbert, D., 47, 304
Hilbert's tenth problem, 46, 47
Hirschberg, D., 305
Hong, J., 298, 304
Hopcroft, J., 90, 143, 198, 247, 267, 302, 304
Hunt, H., 246, 304
Ibarra, O., 143, 304
Immerman, N., 247, 304
initial
	configuration / state, (see configuration / state, initial)
	value of variables, 16, 18
input
	accepted / recognized, 21, 59, 103, 146, 153
	alphabet / symbol, 52 - 53, 97, 146
	head, 55, 95, 145
	node, 275
	nonaccepted / rejected, 21
	of a program, 18
	tape, 55, 95, 145
	value, 18
instance of problem, 31
instantaneous description, (see configuration)
instruction segment, 29
interpretation, 6
intersection, 6, 7, 80 - 81, 130, 143, 193, 300
inverse, 7
Johnson, D., 247, 268, 298, 303, 304
Jones, N., 89, 143, 247, 304, 305
Kannan, R., 298, 305
Karp, R., 246, 305
Kindervater, G., 298, 305
Kleene closure, 7
Kleene, S., 90, 246, 305
knapsack problem, 0 - 1/integer, 221, 244
Kuera, K., 298, 305
Kuroda, S., 47, 198
Laaser, W., 247, 304
Ladner, R., 247, 305
Landweber, P., 198, 305
language, 6 - 7, 11
	accepted / recognized, 29, 61, 259
	decided, 61, 277
	generated, 11, 61
LBA, (see linear bounded automaton)
leaf of graph, 301
left-hand side of production rule, 9
left-linear grammar / language, 72
length of
	derivation, 10
	input / instance, 202 - 203, 205 - 206, 273
	path in graph, 301
	string, 2, 206
Lenstra, J., 298, 305
Lesk, M., 90, 305
Levin, L., 246, 305
Lewis, P., 246, 307
LEX, 74, 90
lexicographically, (see canonically)
linear bounded automaton (LBA), 156, 231
log, 38, 204, 206
logarithmic cost criterion, 201ff.
logspace
	-bounded Turing transducer / machine, 204
	reducibility, 237
LOOP program, 46, 47, 245, 246
lower bound, 211
Lueker, G., 246, 305
Maffioli, F., 268, 305
Matijasevic, Y., 47, 305
max, 301
McCarthy, J., 143, 305
McCulloch, W., 89, 305
Megiddo, N., 297, 305
membership problem, 36, 37, 45, 142, 175 - 177, 186, 195, 197, (see also empty-word membership problem)
Meyer, A., 47, 306
Miller, G., 90, 302
Miller, R., 305
min, 301
mod, 252, 301
Moore, E., 90, 268, 303, 306
move, 56, 99, 149 - 150
Muchnick, S., 89, 143, 304, 305
Muller, D., 297
multiset, 299
Myhill, J., 90, 198, 306
natural number, 299
NC, 289
NLOG, 205, 229, 290
node of graph, 301
nonaccepting computation, (see computation, nonaccepting)
noncomputable function, 35
nondeterministic
	assignment instruction, 17, 24, 26
	computation, (see computation, nondeterministic)
	looping instruction, 17, 22, 26
	program, 18ff., 20, 21ff., 47
	transducer / automaton / machine, 57, 66, 101, 152
nonprimality problem, 242, 251 - 252, 267, (see also primality problem)
NOT gate, 275
NP, 205, 213ff., 246, 264
	-complete / -hard problem, 213 - 225, 244 - 245, 246
NSPACE, 205, 227, 229, 233, 241, 245, 246, 297
NSPACE_ F, 292
NTIME, 205, 225, 227, 233, 241
O notation, 204
Oettinger, A., 143, 306
O'hEigeartaigh, M., 305
one-to-one function, 300
onto function, 300
OR gate, 275
ordered graph, 301
output
	alphabet / symbol, 52 - 53, 97, 147
	head, 55, 95, 145
	node, 275
	of, 21, 59, 103, 153, 258
	tape, 55, 95, 145
	undefined, 21, 59, 103, 153, 258
P, 205, 213, 229, 237 - 238, 291
	-complete / -hard problem, 237 - 238, 246, 247, 291
padded binary representation, (see representation, padded binary)
parallel
	computation thesis, the, 281
	program, 269 - 271
	random access machine (PRAM), 272 - 275, 292 - 298
		COMMON / CREW / PRIORITY, 273
		TOLERANT, 296
Parikh, R., 90, 303
parse graph / tree, 12
partial decidability / solvability, (see decidability)
partially computable function, 35
partition problem, 242, 246
path in graph, 301
PCP, (see Post's correspondence problem)
Perles, M., 90, 143, 198, 302
permutation, 3
phrase structured grammar / language, 8
Pippenger, E., 298, 306
Pitts, W., 89, 305
polylog, 289
polynomial
	expected time bound / complexity, 262
	expression, 45
	space / time  bound / complexity, 203, 262
	time reducibility, 212
pop move, 100
positive closure, 7
Post, E., 198, 306
Post's correspondence problem, 187
power set, 299
PRAM, (see parallel random access machine)
predecessor of node, 301
predicate, 300
prefix, 3
Preparata, F., 297, 306
primality problem, 202, (see also nonprimality problem)
prime number, 202
PRIORITY PRAM, (see parallel random access machine, PRIORITY)
probabilistic
	computation thesis, the, 262
	program, 249
	Turing transducer / machine, (see Turing transducer / machine, probabilistic)
problem, 31
processor, 272
production rule, 8 - 11
program, 16ff., (see also probabilistic program; parallel program)
proper
	prefix / suffix of a string, 3
	subset, 299
PSPACE, 205, 225 - 237, 263
	-complete / -hard problem, 213, 225, 230 - 233, 245, 246
pumping lemma, 75, 90, 123, 143
push move, 100
pushdown
	alphabet / symbol, 109
	head, 95
	store / tape, 95
	transducer / automaton, 95, 109, 130, 133, 142, 143, 191, 192, 197, 260, 267
Rabin, M., 47, 89, 267, 306
Ragde, P., 298, 304
random access machine (RAM), 200 - 201, 246
random assignment instruction, 249
range of function / relation, 300
read instruction, 16, 19
Reckhov, R., 246, 303
recognition problem, 36
recursion in programs, 91 - 93, 143
recursive
	finite-domain program, 92 - 95, 104 - 109, 143
	language, 155, 187, 193
recursively enumerable language, 155, 174, 176, 179, 180, 193
reducibility, 37 - 38, 173, 175, (see also logspace reducibility; polynomial time reducibility)
regular
	expression / set, 73 - 74, 90
	grammar / language, 65ff., 73, 74, 130, 143, 178, 198, 297
reject instruction, 17, 19, 20
rejecting computation, (see nonaccepting computation)
relation, 300
	induced by a problem, 32
	computed by, 29, 61, (see also function computed by)
representation, 5, 39ff., 205 - 206, 277 - 278
	binary, 5
	padded binary, 208
	standard binary, 171 - 172, 174
	unary, 5
reverse of string (rev), 3
right-hand side of production rule, 9
right-linear grammar / language, 72
Rinnooy Kan, A., 305
Ritchie, R., 47, 306
root of graph, 301
rooted graph, 301
Rosier, L., 143, 304
Rozenberg, G., 90, 303
RP, 263 - 265
Ruzzo, L., 298, 306
Sahni, S., 246, 304
satisfiability problem, 215ff., 220ff.
Savitch, W., 246, 306
Scheinberg, S., 143, 306
Schutzenberger, M., 143, 198, 303, 306
Schwartz, J., 268, 306
Scott, D., 47, 89, 306
sentence, 6, 10
	symbol, (see symbol, sentence)
sentential form, 10
sequential computation thesis, the, 204
set, 299
Sethi, R., 302
Shamir, E., 90, 143, 198, 302
Shannon, C., 268, 298, 303, 306
Shapiro, N., 268, 303
Sheperdson, J., 89, 306
Shiloach, Y., 298, 306
single-valuedness problem, 36, 142
Sipser, M., 247, 307
size
	of circuit, 277
	complexity, (see complexity, size)
SIZE, 282, 297
SIZE_ F, 282
Solovay, R., 267, 268, 307
solution for a problem, 32
solvability, 32 - 35, (see also decidability)
space, 200, 201 - 205, 262
	-bounded / complexity, (see complexity, space)
	constructability, 208
	hierarchy, 244
speed-up theorem, linear, 244
Speranza, M., 268, 305
standard binary representation, (see representation, standard binary)
state, 51 - 53, 97, 104, 146
	accepting / initial, 52, 53, 97, 147
Stearns, R., 246, 304, 307
Stockmeyer, L., 247, 298, 302, 307
Strassen, V., 267, 268, 307
string, 2 - 4, 6
	binary, 2
	unary, 2
subgraph, 301
subset, 299
substring, 3
successor of node, 301
suffix, 3
symbol, 2
	auxiliary work-tape / input / output / push- down, (see auxiliary work-tape / input / output / pushdown alphabet)
	blank, 147
	bottom pushdown, 97
	sentence / start, 9
	terminal / nonterminal, 8, 9
	top, 100
Szelepcsenyi, R., 247, 307
Thatcher, J., 305
time, 200, 201 - 205, 262, 273
	-bounded / complexity, (see complexity, time)
	constructibility, 208
	hierarchy, 199, 207, 246
TOLERANT PRAM, (see parallel random access machine, TOLERANT)
total function / relation, 300
transition
	diagram, 53, 97, 147
	rule, 52 - 53, 56 - 57, 97 - 98, 99, 147
	table, 52, 53, 97, 147
Traub, J., 306
traveling-salesperson problem, 242, 246
tree, 301
Turing, A., 47, 197, 307
Turing transducer / machine, 145ff., 155ff., 203ff.
	probabilistic, 258, 259
	universal, 171 - 173, 197, 206 - 207
two-way finite-state automaton, 245, 246
Type 0 grammar / language, 8ff., 9ff., 179ff.
Type 1 grammar / language, 14, 47, 186
Type 2 grammar / language, 14, 111ff.
Type 3 grammar / language, 15, 69ff.
U_ DEPTH, 282, 297
U_ DEPTH_ F, 282
U_ FNC, 289, 292
U_ NC, 238, 289, 290, 291, 297
U_ SIZE, 282
U_ SIZE_ F, 282
U_ SIZE_ DEPTH_ F, 282, 293, 294
Ullman, J., 89, 90, 143, 198, 247, 267, 302, 304
unary alphabet / representation / string, (see alphabet / representation / string, unary)
uncountable set, 301
undecidability, (see decidability)
undefined
	output, (see output, undefined)
	value of function, 300
uniform
	cost criterion, 202ff.
	family of circuits, 280ff.ff., 297
	halting problem, 35
union, 6, 7, 79, 81, 130, 136, 143, 193, 233, 236, 241, 300
universal Turing transducer / machine, (see Turing transducer / machine, universal)
universe, 300
unsolvability, (see solvability)
Valiant, L., 143, 297, 298, 307
Venn diagram, 299
Vercellis, C., 268, 305
vertex of graph, (see node of graph)
Vishkin, U., 298, 302, 306
Welsh, D., 268, 307
word, (see sentence)
write
	conflict, 273
	instruction, 16, 19
Wyllie, J., 298, 303
XOR, 276
ZPP, 263 - 267

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