List of Symbols [a,,.6], 561 [al, ... ,an], 559 Op,32 Onp, 51 A II (Bl, ... , B n ), 290 A(To),537 A*, a*,289 AT, 69 AW (a*; a W ), 354 A®,308 Afin, 386 Ainf,386 .AD,316 (Gl, ... , en) II D, 290 C T ,309 COP, 11 D: n -+ p, 141 D = (a; A; ,), 391, 393, 438 s D = (a; a) : n --+ p, 450 D = (a; A; ,), 313 D:::::: E, 318, 338 D <.......t E, 144 D E, 457 * D E, 457 pT . D --+ E, 317 D E, 144, 317 D.!!.... E, 456 p D --+ E, 456 p D --+ E mod (00, (It), 468 D E, 144 D T ,317 IDI, 141, 313, 391, 393, 438, 450 IDlo, IDh, 391 E = (a; A; 393 E = (,.6; B), 438 EQ(!11),27 E, 27, 42 F" 258 F-ALG, 258 FALSE, 552 FALSEn, 560 FH(T, cp, Err), 584 1(S),346 L(X*),303 Lz,245 £(X*),316 £(X*; X W ), 370 Matr(S; V), 74, 353 Mod (E), 27, 42, 43 Mats, 40, 64 Matsrat«x*)), 335 N,7 REGz and GFz, 246 RL(X*),316 ST'(A)(I,p),520 ST(A)(I,p), 515 S((X*)), 303 SOP, 307 (T,I, t), 128 (T, r, To), 553 (To,A(To»,539
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List of Symbols - Springer978-3-642-78034-9/1.pdf · List of Symbols 613 T(n,p), 32 E~tr, 501 ... ETR, 40 wlp(f, (j), 594 ... Conway semiring module pair, 360 Conway semiring 359
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List of Symbols
[a,,.6], 561 [al, ... ,an], 559 Op,32 Onp, 51 A II (Bl, ... , B n ), 290 A(To),537 A*, a*,289 AT, 69 AW (a*; aW), 354 A®,308 Afin, 386 Ainf,386 .AD,316 (Gl , ... , en) II D, 290 CT ,309 COP, 11
D: n -+ p, 141 D = (a; A; ,), 391, 393, 438
s D = (a; a) : n --+ p, 450 D = (a; A; ,), 313 D:::::: E, 318, 338 D <.......t E, 144 D ~ E, 457
* D ~ E, 457 pT .
D --+ E, 317 D ~ E, 144, 317 D.!!.... E, 456
p D --+ E, 456
p D --+ E mod (00, (It), 468 D ~ E, 144
DT ,317 IDI, 141, 313, 391, 393, 438, 450 IDlo, IDh, 391 E = (a; A; ~), 393 E = (,.6; B), 438 EQ(!11),27 E, 27, 42
293 simulation, 144 small category, 11 Soundness Theorem, 585 source pairing, 48 source tupling, 32 standard model of Peano arith-
metic, 611 star commutative identity, 292 star fixed point identity, 291 star pairing identity, 291 star permutation identity, 291 star product identity, 291 star sum identity, 291 star theory, 290 star theory morphism, 290 star zero identity, 291 strict ordered theory, 244 strong functorial dagger, 176 strong iteration algebra, 235 subalgebra, 24 subalgebras, quotients and prod-
248 w-diagram, 13 w-idempotent grove iteration the
ory, 532
Zero Congruence Lemma, 202 zero identities, 131 zero morphisms, 49
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EATCS Monographs on Theoretical Computer Science
Vol. I: K. Mehlhorn Data Structures and Algorithms 1: Sorting and Searching
Vol. 2: K. Mehlhorn Data Structures and Algorithms 2: Graph Algorithms and NP-Completeness
Vol. 3: K. Mehlhorn Data Structures and Algorithms 3: Multidimensional Searching and Computational Geometry
Vol. 4: W. Reisig Petri Nets An Introduction
Vol. 5: W. Kuich, A. Salomaa Semirings, Automata, Languages
Vol. 6: H. Ehrig, B. Mahr Fundamentals of Algebraic Specification 1 Equations and Initial Semantics
Vol. 7: F. Gecseg Products of Automata
Vol. 8: F. Kroger Temporal Logic of Programs
Vol. 9: K. Weihrauch Computability
Vol. 10: H. Edelsbrunner Algorithms in Combinatorial Geometry
Vol. II: J. L. Ba1cazar, J. Diaz, J. Gabarr6 Structural Complexity I
Vol. 12: J. Berstel, C. Reutenauer Rational Series and Their Languages
Vol. 13: E. Best, C. Fernandez C. Nonsequential Processes A Petri Net View
Vol. 14: M. Jantzen Confluent String Rewriting
Vol. IS: S. Sippu, E. Soisalon-Soininen Parsing Theory Volume I: Languages and Parsing
Vol. 16: P. Padawitz Computing in Horn Clause Theories
Vol. 17: J. Paredaens, P. DeBra, M. Gyssens, D. Van Gucht The Structure of the Relational Database Model
Vol. 18: J. Dassow, G. Paun Regulated Rewriting in Formal Language Theory
Vol. 19: M. Tofte Compiler Generators What they can do, what they might do, and what they will probably never do
Vol. 20: S. Sippu, E. Soisalon-Soininen Parsing Theory Volume II: LR(k) and LL(k) Parsing
Vol. 21: H. Ehrig, B. Mahr Fundamentals of Algebraic Specification 2 Module Specifications and Constraints
Vol. 22: J. L Ba1cazar, J. Diaz, J. Gabarr6 Structural Complexity II
Vol. 23: A. Salomaa Public-Key Cryptography
Vol. 24: T. Gergely, L. Dry First-Order Programming Theories
Vol. 25: W. Wechler Universal Algebra for Computer Scientists
EATCS Monographs on Theoretical Computer Science
R. Janicki, P. E. Lauer Specification and Analysis of Concurrent Systems The COSY Approach
O. Watanabe (Ed.) Kolmogorov Complexity and Computational Complexity
K. Jensen Coloured Petri Nets Basic Concepts, Analysis Methods and Practical Use, Vol. 1
G. Schmidt, Th. Strohlein Relations and Graphs Discrete Mathematics for Computer Scientists
S. L. Bloom, Z. Esik Iteration Theories The Equational Logic of Iterative Processes