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Perfect play for a game is known when the game is solved. [1] Based on the rules of a game, every possible final position can be evaluated (as a win, loss or draw). By backward reasoning, one can recursively evaluate a non-final position as identical to the position that is one move away and best valued for the player whose move it is. Thus a ...
A formula game is an artificial game represented by a fully quantified Boolean formula such as …. One player (E) has the goal of choosing values so as to make the formula ψ {\displaystyle \psi } true, and selects values for the variables that are existentially quantified with ∃ {\displaystyle \exists } .
The Bellman equation is classified as a functional equation, because solving it means finding the unknown function , which is the value function. Recall that the value function describes the best possible value of the objective, as a function of the state . By calculating the value function, we will also find the function () that describes the ...
Microsoft Excel is a spreadsheet editor developed by Microsoft for Windows, macOS, Android, iOS and iPadOS.It features calculation or computation capabilities, graphing tools, pivot tables, and a macro programming language called Visual Basic for Applications (VBA).
In a programming language, an evaluation strategy is a set of rules for evaluating expressions. [1] The term is often used to refer to the more specific notion of a parameter-passing strategy [2] that defines the kind of value that is passed to the function for each parameter (the binding strategy) [3] and whether to evaluate the parameters of a function call, and if so in what order (the ...
For example, in the expression (f(x)-1)/(f(x)+1), the function f cannot be called only once with its value used two times since the two calls may return different results. Moreover, in the few languages which define the order of evaluation of the division operator's operands, the value of x must be fetched again before the second call, since ...
The value function of an optimization problem gives the value attained by the objective function at a solution, while only depending on the parameters of the problem. [1] [2] In a controlled dynamical system, the value function represents the optimal payoff of the system over the interval [t, t 1] when started at the time-t state variable x(t)=x. [3]
In the example above, + is an associative operation, so the final result will be the same regardless of parenthesization, although the specific way in which it is calculated will be different. In the general case of non-associative binary functions, the order in which the elements are combined may influence the final result's value.