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Algebraic laws for nondeterminism and concurrency
 Journal of the ACM
, 1985
"... Abstract. Since a nondeterministic and concurrent program may, in general, communicate repeatedly with its environment, its meaning cannot be presented naturally as an input/output function (as is often done in the denotational approach to semantics). In this paper, an alternative is put forth. Firs ..."
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Cited by 608 (13 self)
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observation congruence class. The paper demonstrates, for a sequence of simple languages expressing finite (terminating) behaviors, that in each case observation congruence can be axiomatized algebraically. Moreover, with the addition of recursion and another simple extension, the algebraic language described
Algebraic Laws for Feature Models
"... Abstract: Software Product Lines (SPL) may be adopted by either bootstrapping existing software products into a SPL, or extending an existing SPL to encompass an additional software product. Program refactorings are usually applied for carrying out those tasks. The notion of SPL refactoring is an ex ..."
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Cited by 6 (1 self)
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. In this paper, we propose a complete, sound catalog of algebraic laws, making up special FM refactorings that preserve configurability. This catalog is also defined as minimal, as one law cannot be derived from another one in the same catalog. In addition, a theory for FMs is presented, in the context of a
Exploiting algebraic laws to improve mechanized axiomatizations
 In: Proc. CALCO’13. LNCS
, 2013
"... Abstract. In the field of structural operational semantics (SOS), there have been several proposals both for syntactic rule formats guaranteeing the validity of algebraic laws, and for algorithms for automatically generating groundcomplete axiomatizations. However, there has been no synergy betwee ..."
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Cited by 1 (0 self)
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Abstract. In the field of structural operational semantics (SOS), there have been several proposals both for syntactic rule formats guaranteeing the validity of algebraic laws, and for algorithms for automatically generating groundcomplete axiomatizations. However, there has been no synergy
Uniqueness of Certain Algebraic Laws on Cubic Curves
"... . An nary Steiner law f(x 1 ; x 2 ; \Delta \Delta \Delta ; x n ) on a projective curve \Gamma over an algebraically closed field k is a totally symmetric nary morphism f from \Gamma n to \Gamma satisfying the universal identity f(x 1 ; x 2 ; \Delta \Delta \Delta ; x n\Gamma1 ; f(x 1 ; x 2 ; \De ..."
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. An nary Steiner law f(x 1 ; x 2 ; \Delta \Delta \Delta ; x n ) on a projective curve \Gamma over an algebraically closed field k is a totally symmetric nary morphism f from \Gamma n to \Gamma satisfying the universal identity f(x 1 ; x 2 ; \Delta \Delta \Delta ; x n\Gamma1 ; f(x 1 ; x 2
Generating Algebraic Laws from Imperative Programs
 Theoretical Computer Science
, 1999
"... Abstract. The use of veri ers for proving the correctness of concrete programs is well known and has been amply described in the literature. Here we focus on further, perhaps more general tasks such veri ers can perform. Given a program that is assumed to be correct, we derive a set of axioms for th ..."
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Cited by 2 (0 self)
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Abstract. The use of veri ers for proving the correctness of concrete programs is well known and has been amply described in the literature. Here we focus on further, perhaps more general tasks such veri ers can perform. Given a program that is assumed to be correct, we derive a set of axioms for the data structures involved. In the simplest case, we studyanabstract program interchanging the contents of two variables. The veri cation conditions generated by our veri er, NPPV, are a set of equations specifying quasigroups. Other examples reveal the notion of \strategy " from the veri cation of an abstract game playing program, or show the correspondence between inductive proofs of numeric properties and veri cation of a program searching for a counterexample. Finally we apply NPPV on Wand's example showing the incompleteness of Hoare's logic. We alsogive a simpli ed proof of Wand's result. 1 Algorithm = Data Structure + Control According tostandard de nitions [4], an algorithm is a detailed and explicit
Automated Code Generator Verification Based on Algebraic Laws
, 1995
"... ing from Machine Details In order to derive a verified compiler, MullerOlm first defines the effect of target machine (in this case transputer) instructions by simple source language processes, consisting mainly of delays indicating time consumption (as taken from the reference manual [Inm88]), as ..."
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Cited by 2 (0 self)
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ing from Machine Details In order to derive a verified compiler, MullerOlm first defines the effect of target machine (in this case transputer) instructions by simple source language processes, consisting mainly of delays indicating time consumption (as taken from the reference manual [Inm88]), assignments to variables representing the machine state, and some assertions. As an example, let us look at the definition of the effect of "jump" instructions: E 0 (j) w \Delta 3 ; IP; A; B; C; OReg:= IP + OReg; ?; ?; ?; 0 (1) This refinement relationship expresses that one may assume at least (w) the following about the basic effect (E 0 ) of a jump instruction (whose mnemonic is j): It takes up to 3 clock cycles, adds the contents of the operand register to the instruction pointer, makes the registers A, B, and C undefined, and clears the operand register. After this machine level has been defined, abstractions are introduced that correspond to increasingly abstract assembler languages. Th...
Reevaluating Amdahl’s law
 Commun. ACM
, 1988
"... At Sandia National Laboratories, we are currently engaged in research involving massively parallel processing. There is considerable skepticism regarding the viability of massive parallelism; the skepticism centers around Amdahl’s law, an argument put forth by Gene Amda.hl in 1967 [l] that even w ..."
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Cited by 316 (4 self)
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, then Amdahl’s law says that speedup is given by Speedup = (s + p)/(s + p/N) = l/b + p/N), where we have set total time s + p = 1 for algebraic simphcity. For N = 1024 this is an unforgivingly steep function of s near s = 0 (see Figure 1). The steepness of the graph near s = 0 (approximatelyN’) implies
Programming with bananas, lenses, envelopes and barbed wire
 In FPCA
, 1991
"... We develop a calculus for lazy functional programming based on recursion operators associated with data type definitions. For these operators we derive various algebraic laws that are useful in deriving and manipulating programs. We shall show that all example Functions in Bird and Wadler's &qu ..."
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Cited by 329 (11 self)
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We develop a calculus for lazy functional programming based on recursion operators associated with data type definitions. For these operators we derive various algebraic laws that are useful in deriving and manipulating programs. We shall show that all example Functions in Bird and Wadler
Some Algebraic Laws for Spans (and Their Connections With MultiRelations)
 Proceedings of RelMiS 2001, Workshop on Relational Methods in Software. Electronic Notes in Theoretical Computer Science, n.44 v.3, Elsevier Science (2001
, 2001
"... This paper investigates some basic algebraic properties of the categories of spans and cospans (up to isomorphic supports) over the category Set of (small) sets and functions, analyzing the monoidal structures induced over both spans and cospans by the cartesian product and disjoint union of sets. O ..."
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Cited by 10 (3 self)
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This paper investigates some basic algebraic properties of the categories of spans and cospans (up to isomorphic supports) over the category Set of (small) sets and functions, analyzing the monoidal structures induced over both spans and cospans by the cartesian product and disjoint union of sets
Results 1  10
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