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Fractal Symbolic Analysis
, 2001
"... Modern compilers perform wholesale restructuring of programs to improve their efficiency. Dependence analysis is the most widely used technique for proving the correctness of such transformations, but it suffers from the limitation that it considers only the memory locations read and written by a st ..."
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Cited by 17 (2 self)
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Modern compilers perform wholesale restructuring of programs to improve their efficiency. Dependence analysis is the most widely used technique for proving the correctness of such transformations, but it suffers from the limitation that it considers only the memory locations read and written by a
Fractal Symbolic Analysis for Program Transformations
 IN ACM INTERNATIONAL CONFERENCE ON SUPERCOMPUTING (ICS) 2001. ACM
, 2000
"... Restructuring compilers use dependence analysis to prove that the meaning of a program is not changed by a transformation. A wellknown limitation of dependence analysis is that it examines only the memory locations read and written by a statement, and does not assume any particular interpretation f ..."
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Cited by 5 (4 self)
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Restructuring compilers use dependence analysis to prove that the meaning of a program is not changed by a transformation. A wellknown limitation of dependence analysis is that it examines only the memory locations read and written by a statement, and does not assume any particular interpretation
Leftlooking to rightlooking and vice versa: An application of fractal symbolic analysis to linear algebra code restructuring
 In Proceedings of EuroPar
, 2000
"... Abstract. We have recently developed a new program analysis strategy called fractal symbolic analysis that addresses some of limitations of techniques such as dependence analysis. In this paper, we showhow fractal symbolic analysis can be used to convert between leftlooking and rightlooking versio ..."
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Cited by 3 (3 self)
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Abstract. We have recently developed a new program analysis strategy called fractal symbolic analysis that addresses some of limitations of techniques such as dependence analysis. In this paper, we showhow fractal symbolic analysis can be used to convert between leftlooking and right
Look Left, Look Right, Look Left Again: An Application of Fractal Symbolic Analysis to Linear Algebra Code Restructuring
 Int. J. Parallel Comput
, 2003
"... Fractal symbolic analysis is a symbolic analysis technique for verifying the legality of program transformations. It is strictly more powerful than dependence analysis# for example, it can be used to verify the legalityofblocking LU factorization with pivoting, a task for which dependence analys ..."
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Cited by 3 (0 self)
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Fractal symbolic analysis is a symbolic analysis technique for verifying the legality of program transformations. It is strictly more powerful than dependence analysis# for example, it can be used to verify the legalityofblocking LU factorization with pivoting, a task for which dependence
Left to Right and vice versa: Applying Fractal Symbolic Analysis to Restructuring Linear Algebra Codes
"... . We have recently developed a new program analysis strategy called fractal symbolic analysis that addresses some of limitations of techniques such as dependence analysis. In this paper, we show how fractal symbolic analysis can be used to convert between leftlooking and rightlooking versions o ..."
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. We have recently developed a new program analysis strategy called fractal symbolic analysis that addresses some of limitations of techniques such as dependence analysis. In this paper, we show how fractal symbolic analysis can be used to convert between leftlooking and rightlooking versions
The Symbol Grounding Problem
, 1990
"... There has been much discussion recently about the scope and limits of purely symbolic models of the mind and about the proper role of connectionism in cognitive modeling. This paper describes the "symbol grounding problem": How can the semantic interpretation of a formal symbol system be m ..."
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Cited by 1072 (18 self)
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There has been much discussion recently about the scope and limits of purely symbolic models of the mind and about the proper role of connectionism in cognitive modeling. This paper describes the "symbol grounding problem": How can the semantic interpretation of a formal symbol system
Symbolic Model Checking for Realtime Systems
 INFORMATION AND COMPUTATION
, 1992
"... We describe finitestate programs over realnumbered time in a guardedcommand language with realvalued clocks or, equivalently, as finite automata with realvalued clocks. Model checking answers the question which states of a realtime program satisfy a branchingtime specification (given in an ..."
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Cited by 574 (50 self)
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in an extension of CTL with clock variables). We develop an algorithm that computes this set of states symbolically as a fixpoint of a functional on state predicates, without constructing the state space. For this purpose, we introduce a calculus on computation trees over realnumbered time. Unfortunately
Culture in action: Symbols and strategies
 American Sociological Review
, 1986
"... Culture influences action not by providing the ultimate values toward which action is oriented, but by shaping a repertoire or "tool kit " of habits, skills, and styles from which people construct "strategies of action. " Two models of cultural influence are developed, for settle ..."
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Cited by 455 (0 self)
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Culture influences action not by providing the ultimate values toward which action is oriented, but by shaping a repertoire or "tool kit " of habits, skills, and styles from which people construct "strategies of action. " Two models of cultural influence are developed, for settled and unsettled cultural periods. In settled periods, culture independently influences action, but only by providing resources from which people can construct diverse lines of action. In unsettled cultural periods, explicit ideologies directly govern action, but structural opportunities for action determine which among competing ideologies survive in the long run. This alternative view of culture offers new opportunities for systematic, differentiated arguments about culture's causal role in shaping action. The reigning model used to understand culture's effects on action is fundamentally misleading. It assumes that culture shapes action by supplying ultimate ends or values toward which action is directed, thus making values
The algorithmic analysis of hybrid systems
 THEORETICAL COMPUTER SCIENCE
, 1995
"... We present a general framework for the formal specification and algorithmic analysis of hybrid systems. A hybrid system consists of a discrete program with an analog environment. We model hybrid systems as nite automata equipped with variables that evolve continuously with time according to dynamica ..."
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Cited by 783 (76 self)
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to linear hybrid systems. In particular, we consider symbolic modelchecking and minimization procedures that are based on the reachability analysis of an infinite state space. The procedures iteratively compute state sets that are definable as unions of convex polyhedra in multidimensional real space. We
Convex Analysis
, 1970
"... In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a lo ..."
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Cited by 5350 (67 self)
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In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a
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