### Table 43: Overview of axioms of concurrent process algebras.

1996

"... In PAGE 131: ... We have the following legend: A indicates that the axiom is present in the theory, A indicates that the axiom is not present but can be derived (for closed terms) from the other axioms in the theory, A indicates that the axiom does not hold in the theory, A indicates that the axiom is meaningless in the theory, as there is a signature conflict. In Table43 on page 135 we give an overview of the axioms pertaining to merge operators of the (concurrent) process algebras treated in Section 3. The legend is the same as for the previous table.... ..."

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### Table 1: Basic process algebra with autonomous actions

1995

"... In PAGE 2: ...ur basic algebra BPAaa is an extensionof BPA : basic process algebra with inaction (c.f. [BaWe90]). The signature and axioms are given in Table1 . First, in the header, the sort of atoms (A) is declared, which is a parameter of the theory.... In PAGE 2: ... The I axioms (for inequality ) state that unstable nondeterminism may be reduced in an implemen- tation. The algebra BPAaa is obtained from BPAaa by removing these inequalities from the axioms in Table1 . Note that BPAaa with atoms A equals BPA with atoms AC.... ..."

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### TABLE I 1-D DISCRETE INFINITE AND FINITE TIME AND SPACE SIGNAL PROCESSING AS FOUR INSTANTIATIONS OF THE GENERAL ALGEBRAIC THEORY. THE BOLDED CONCEPTS ARE SUPPLIED BY THE ALGEBRAIC THEORY.

2006

### Table 1. The nondeterministic relation

"... In PAGE 7: ...Table1 . Note that the symmetric versions of rules (Sum) and (Par1) have been omitted.... In PAGE 7: ... Thus, by rule (Act2) we have (P; fr1; r2g) f(r1;2);(r2;3)g ?! (Q; ;), whereas (P; fr1; r2g), (P; fr1; r2g), and (P; fr1; r2g) have no transitions. Except for the appearance of worlds in con- gurations, the rules of Table1 are essentially identical to the ones for ACSR. It is worth pointing out that all processes in a parallel composition need to... ..."

### Table 6: Inequations for sequential, nondeterministic processes

"... In PAGE 15: ... We shall write E1 vCP E2 (E1 =CP E2) to indicate that E1 v E2 (E1 = E2) can be derived within CP. Table6 contains the standard inequations for testing from [20, 28]. The laws in Table 7 state that process is less de ned than every PAL process (UND1) and assert the strictness of all binary operators (strictness of follows from IC4).... ..."

### Table 6: Inequations for sequential, nondeterministic processes

"... In PAGE 15: ... We shall write E1 vCP E2 (E1 =CP E2) to indicate that E1 v E2 (E1 = E2) can be derived within CP. Table6 contains the standard inequations for testing from [21, 30]. The laws in Table 7 state that process is less de ned than every PAL process (UND1) and assert the strictness of all binary operators (strictness of follows from IC4).... ..."

### Table 1. Axioms for the algebraic theory of the language

"... In PAGE 14: ...1. The axioms for the algebraic theory of the language are given in Table1 . In the de nition we assume ADSeq(d), ADSeq(di), ASeq(w) and ASeq(wi) for i = 1; 2.... In PAGE 14: ... Note that we do not have an axiom x+y = y +x. This equality is derivable using the axioms in Table1 , in particular, Axiom 1. The axioms in the above de nition are not su cient to prove equality of programs like ha; b; ci and ha; hb; cii.... ..."

### Table 4: Process Algebra Formalisms

1997

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