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52
Dynamic Logic
 Handbook of Philosophical Logic
, 1984
"... ed to be true under the valuation u iff there exists an a 2 N such that the formula x = y is true under the valuation u[x=a], where u[x=a] agrees with u everywhere except x, on which it takes the value a. This definition involves a metalogical operation that produces u[x=a] from u for all possibl ..."
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Cited by 823 (7 self)
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ed to be true under the valuation u iff there exists an a 2 N such that the formula x = y is true under the valuation u[x=a], where u[x=a] agrees with u everywhere except x, on which it takes the value a. This definition involves a metalogical operation that produces u[x=a] from u for all possible values a 2 N. This operation becomes explicit in DL in the form of the program x := ?, called a nondeterministic or wildcard assignment. This is a rather unconventional program, since it is not effective; however, it is quite useful as a descriptive tool. A more conventional way to obtain a square root of y, if it exists, would be the program x := 0 ; while x < y do x := x + 1: (1) In DL, such programs are firstclass objects on a par with formulas, complete with a collection of operators for forming compound programs inductively from a basis of primitive programs. To discuss the effect of the execution of a program on the truth of a formula ', DL uses a modal construct <>', which
DecisionTheoretic Deliberation Scheduling for Problem Solving In . . .
 ARTIFICIAL INTELLIGENCE
, 1994
"... We are interested in the problem faced byanagent with limited computational capabilities, embedded in a complex environment with other agents and processes not under its control. Careful management of computational resources is important for complex problemsolving tasks in which the time spent in ..."
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Cited by 157 (3 self)
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We are interested in the problem faced byanagent with limited computational capabilities, embedded in a complex environment with other agents and processes not under its control. Careful management of computational resources is important for complex problemsolving tasks in which the time spent in decision making affects the quality of the responses generated by a system.
A NestedGraph Model for the Representation and Manipulation of Complex Objects
 ACM Transactions on Information Systems
, 1994
"... this paper we report upon a graphbased approach to such an integration. Our use of graphs has two key advantages : firstly, graphs are formally defined, wellunderstood structures; secondly, it is widely accepted that graphbased formalisms considerably enhance the usability of complex systems [19] ..."
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Cited by 36 (4 self)
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this paper we report upon a graphbased approach to such an integration. Our use of graphs has two key advantages : firstly, graphs are formally defined, wellunderstood structures; secondly, it is widely accepted that graphbased formalisms considerably enhance the usability of complex systems [19]. Graphs have been used in conjunction with a number of conventional data models, for example the hierarchical and network models [35], the entityrelationship model [9] and a recent extension thereof for complex objects [27], and various semantic data models [16, 20, 31]. Graphs or hypergraphs [6] have also been used more recently in [12, 17, 23, 25, 33, 36] as a data modelling tool in their own right. We give a comparison between this recent work and our own approach in Section 4 of the paper. Directed graphs have also been the foundation of Hypertext databases [11, 33]. Such databases are graphs consisting of nodes which refer to units of stored information (typically text) and of named links. Each link connects two nodes, the "source" and the "destination". Links are traversed either forwards (from source to destination) or backwards (from destination to source). The process of traversing named links and examining the text associated with nodes is called
Beyond The Universal Turing Machine
, 1998
"... We describe an emerging field, that of nonclassical computability and nonclassical computing machinery. According to the nonclassicist, the set of welldefined computations is not exhausted by the computations that can be carried out by a Turing machine. We provide an overview of the field and a phi ..."
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Cited by 28 (1 self)
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We describe an emerging field, that of nonclassical computability and nonclassical computing machinery. According to the nonclassicist, the set of welldefined computations is not exhausted by the computations that can be carried out by a Turing machine. We provide an overview of the field and a philosophical defence of its foundations.
Parallel RealTime Optimization: Beyond Speedup
 PARALLEL PROCESSING LETTERS
, 1999
"... Traditionally, interest in parallel computation centered around the speedup provided by parallel algorithms over their sequential counterparts. In this paper, we ask a different type of question: Can parallel computers, due to their speed, do more than simply speed up the solution to a problem? ..."
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Cited by 25 (23 self)
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Traditionally, interest in parallel computation centered around the speedup provided by parallel algorithms over their sequential counterparts. In this paper, we ask a different type of question: Can parallel computers, due to their speed, do more than simply speed up the solution to a problem? We show that for realtime optimization problems, a parallel computer can obtain a solution that is better than that obtained by a sequential one. Specifically, a sequential and a parallel algorithm are exhibited for the problem of computing the bestpossible approximation to the minimumweight spanning tree of a connected, undirected and weighted graph whose vertices and edges are not all available at the outset, but instead arrive in real time. While the parallel algorithm succeeds in computing the exact minimumweight spanning tree, the sequential algorithm can only manage to obtain an approximate solution. In the worst case, the ratio of the weight of the solution obtained seque...
Reasoning about Action and Change  A Dynamic Logic Approach
 Journal of Logic, Language, and Information
, 1996
"... this paper, we pursue a monotonic approach to the frame problem and concentrate on the combinatorial problem and the overcommitment problem. We will propose a solution within the framework of propositional dynamic logic (PDL)the modal logic of actions and of computer programs (see Pratt, 1976, 19 ..."
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Cited by 24 (0 self)
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this paper, we pursue a monotonic approach to the frame problem and concentrate on the combinatorial problem and the overcommitment problem. We will propose a solution within the framework of propositional dynamic logic (PDL)the modal logic of actions and of computer programs (see Pratt, 1976, 1980; Segerberg 1980; Harel, 1984). It is based on the idea of associating an operator [ff] with each action ff, the brackets being reminiscient of the box operator 2 of ordinary modal logic (see Hughes & Cresswell, 1984). The reading of a formula [ff]A is "after every terminating (halting) execution of ff, A is true." PDL provides a powerful language for describing compound actions such as sequential composition of actions ff and fi, written ff; fi, (nondeterministic) choice between ff and fi, written ff + fi, and (nondeterministic) iteration of ff, written ff
Solving TimeDependent Problems: A DecisionTheoretic Approach to Planning in Dynamic Environments
, 1991
"... Controlling a robot involves making decisions that modify its behavior. Making good decisions may require timeconsuming computation. Changes in the environment over time affect when this computation can be done (e.g., after obtaining the necessary information) , and when a result is useful (e.g., b ..."
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Cited by 15 (1 self)
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Controlling a robot involves making decisions that modify its behavior. Making good decisions may require timeconsuming computation. Changes in the environment over time affect when this computation can be done (e.g., after obtaining the necessary information) , and when a result is useful (e.g., before some event occurs). This sensitivity to when computation is performed and when decisions are made is what makes these problems "timedependent." A controller with more than one decision to make must trade off computation time, based on the expected effect on the system's behavior. We call the resulting metalevel scheduling problem a "deliberationscheduling" problem. We have
Sharing of Computations
, 1993
"... This report is a revised version of my thesis of the same title, which was accepted for the Ph.D. degree in Computer Science at University of Aarhus, Denmark, in June 1993 ..."
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Cited by 15 (3 self)
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This report is a revised version of my thesis of the same title, which was accepted for the Ph.D. degree in Computer Science at University of Aarhus, Denmark, in June 1993
Parallel RealTime Computation: Sometimes Quantity Means Quality
 Computing and Informatics
, 2000
"... The primary purpose of parallel computation is the fast execution of computational tasks that are too slow to perform sequentially. As a consequence, interest in parallel computation to date has naturally focused on the speedup provided by parallel algorithms over their sequential counterparts. Th ..."
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Cited by 14 (13 self)
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The primary purpose of parallel computation is the fast execution of computational tasks that are too slow to perform sequentially. As a consequence, interest in parallel computation to date has naturally focused on the speedup provided by parallel algorithms over their sequential counterparts. The thesis of this paper is that a second equally important motivation for using parallel computers exists. Specifically, the following question is posed: Can parallel computers, thanks to their multiple processors, do more than simply speed up the solution to a problem? We show that within the paradigm of realtime computation, some classes of problems have the property that a solution to a problem in the class, when computed in parallel, is far superior in quality than the best one obtained on a sequential computer. What constitutes a better solution depends on the problem under consideration. Thus, `better' means `closer to optimal' for optimization problems, `more secure' for crypto...
Parallel RealTime Numerical Computation: Beyond Speedup III
 International Journal of Computers and their Applications, Special Issue on High Performance Computing Systems
"... Parallel computers can do more than simply speed up sequential computations. They are capable of finding solutions that are far better in quality than those obtained by sequential computers. This fact is demonstrated by analyzing sequential and parallel solutions to numerical problems in a realtime ..."
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Cited by 14 (13 self)
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Parallel computers can do more than simply speed up sequential computations. They are capable of finding solutions that are far better in quality than those obtained by sequential computers. This fact is demonstrated by analyzing sequential and parallel solutions to numerical problems in a realtime paradigm. In this setting, numerical data required to solve a problem are received as input by a computer system, at regular intervals. The computer must process its inputs as soon as they arrive. It must also produce its outputs at regular intervals, as soon as they are available. We show that for some realtime numerical problems a parallel computer can deliver a solution that is significantly more accurate than when computed by a sequential computer. Similar results were derived recently in the areas of realtime optimization and realtime cryptography. Key words and phrases: Parallelism, realtime computation, numerical analysis. This research was supported by the Natural Sciences a...