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Model-Checking One-Clock Priced Timed Automata
Model-Checking One-Clock Priced Timed Automata

... For each index i, we restrict the automaton A to transitions whose guards contain the interval (ai , ai+1 ), and that do not reset the clock. We denote by Ai this restricted automaton. Let q and q ′ be two locations of Ai . As stated by the following lemma, the set of costs of paths between (q, ai ) ...


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... (E) interacting particle systems have been considered to approximate πt non-parametrically via simulation tools [7, 8, 9, 12]. The optimal stopping sub-problem of the second step can again be tackled within several frameworks. When the transition density of the state variables is known, classical ( ...
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... Saylor URL : www.saylor.org/courses/ma111 © 2011 Harold Reiter This material may be copied, stored and distributed for non-commercial purposes only. Any commercial use of this material is strictly forbidden. ...
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... is a natural approach for tackling large scale problems. Cooperative Co-evolution (CC) [15] is such a technique that decomposes a large scale problem into a set of sub-problems, each of which is optimised using a separate EA. In the original CC decomposition strategy, each variable is placed in a se ...
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Algorithm



In mathematics and computer science, an algorithm (/ˈælɡərɪðəm/ AL-gə-ri-dhəm) is a self-contained step-by-step set of operations to be performed. Algorithms exist that perform calculation, data processing, and automated reasoning.An algorithm is an effective method that can be expressed within a finite amount of space and time and in a well-defined formal language for calculating a function. Starting from an initial state and initial input (perhaps empty), the instructions describe a computation that, when executed, proceeds through a finite number of well-defined successive states, eventually producing ""output"" and terminating at a final ending state. The transition from one state to the next is not necessarily deterministic; some algorithms, known as randomized algorithms, incorporate random input.The concept of algorithm has existed for centuries, however a partial formalization of what would become the modern algorithm began with attempts to solve the Entscheidungsproblem (the ""decision problem"") posed by David Hilbert in 1928. Subsequent formalizations were framed as attempts to define ""effective calculability"" or ""effective method""; those formalizations included the Gödel–Herbrand–Kleene recursive functions of 1930, 1934 and 1935, Alonzo Church's lambda calculus of 1936, Emil Post's ""Formulation 1"" of 1936, and Alan Turing's Turing machines of 1936–7 and 1939. Giving a formal definition of algorithms, corresponding to the intuitive notion, remains a challenging problem.
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