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Exploiting Bounds in Operations Research and Artificial Intelligence
Exploiting Bounds in Operations Research and Artificial Intelligence

... Duality theory Associated with any minimization LP is its dual problem, which is a maximization LP [22]. After solving an LP, the dual supplies bounds on changes that can be made to coefficients in the original problem without affecting optimality. These bounds are used for sensitivity analysis, an ...
Ch2-Sec 2.3
Ch2-Sec 2.3

Lecture 0 - School of Computing
Lecture 0 - School of Computing

M-100 2-1 Solve 1-2 Eq Lec.cwk (WP)
M-100 2-1 Solve 1-2 Eq Lec.cwk (WP)

... we do not know if the left and right sides of the equation are equal to each other. We will now learn how to find the value for x that will make the left and right sides of the equation are equal to each other. We call this process finding a solution to an equation. We also say that we are solving t ...
Answer - West Jefferson Local Schools
Answer - West Jefferson Local Schools

... you are working on. If you accessed a feature, this button will return you to the slide from where you accessed the feature. Click the Main Menu button to return to the presentation main menu. Click the Help button to access this screen. Click the Exit button or press the Escape key [Esc] to end the ...
Document
Document

y + 2z = 13 + - Adjective Noun Math
y + 2z = 13 + - Adjective Noun Math

Document
Document

pdf
pdf

Planning with Specialized SAT Solvers
Planning with Specialized SAT Solvers

... The priority queue is controlled by a heuristic that orders the subgoals. When the preconditions of an action at time t become new subgoals and are pushed into the queue, we give a preference to the precondition which must have been true longer before t (i.e. its value is true for a higher number of ...
Simulated Annealing - School of Computer Science
Simulated Annealing - School of Computer Science

... The starting temperature must be hot enough to allow a move to almost any neighbourhood state. If this is not done then the ending solution will be the same (or very close) to the starting solution. Alternatively, we will simply implement a hill climbing algorithm. However, if the temperature starts ...
Planning with Specialized SAT Solvers
Planning with Specialized SAT Solvers

... The variable selection scheme (Rintanen a2010) is based on the following observation: each of the goal literals has to be made true by an action, and the precondition literals of each such action have to be made true by earlier actions (or, alternatively, these literals have to be true in the initia ...
The Redundancy Queuing-Location-Allocation Problem: A Novel
The Redundancy Queuing-Location-Allocation Problem: A Novel

Rates and Unit Analysis
Rates and Unit Analysis

parsing with flexibility, dynamic strategies, and idioms in mind
parsing with flexibility, dynamic strategies, and idioms in mind

Lesson 3-1 Powerpoint - peacock
Lesson 3-1 Powerpoint - peacock

... Since (1 , 2) makes both equations true, then (1 , 2) is the solution to the system of linear equations. ...
Project specification
Project specification

No Slide Title
No Slide Title

... Equation 2 because the x-coefficient was 1. In general you should solve for a variable whose coefficient is 1 or –1. CHOOSING A METHOD ...
Solve the equation.
Solve the equation.

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Clausal Connection-Based Theorem Proving in
Clausal Connection-Based Theorem Proving in

mathematical origins of
mathematical origins of

... variable and today are called partial differential equations. Newton would express the right side of the equation in powers of the dependent variables and assumed as a solution an infinite series. The coefficients of the infinite series were then determined [23]. Even though Newton noted that the co ...
On the Brahmagupta–Fermat–Pell Equation x2 dy2 = ±1 - IMJ-PRG
On the Brahmagupta–Fermat–Pell Equation x2 dy2 = ±1 - IMJ-PRG

pdf [local copy]
pdf [local copy]

... extent) the rules of inference apply also to the new kind of expressions, it is necessary to have a survey of all possible expressions, and this can be furnished only by syntactical considerations. The matter is especially doubtful for the rule of substitution and of replacing defined symbols by the ...
Notes on Simply Typed Lambda Calculus
Notes on Simply Typed Lambda Calculus

... Let r1 and r2 be terms with path(r1 ) = path(r2 ). (1) Take σ ∈ path(r1 ) = path(r2 ) and let s1 and s2 be the corresponding sub-terms occurring at σ. Show that s1 and s2 are either both variables, or both applications, or both abstractions. Show that the two parts of 2. in the definition of ≡α are ...
An Efficient Hardware Implementation for AI applications
An Efficient Hardware Implementation for AI applications

... The basic innovation of the top-down parser that Earley [18], was the introduction of a symbol called dot “•” that does not belong to the grammar. The utility of the dot in a rule (now called dotted rule) is to separate the right part of the rule into two subparts. For the subpart at the left of the ...
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Unification (computer science)

Unification, in computer science and logic, is an algorithmic process of solving equations between symbolic expressions.Depending on which expressions (also called terms) are allowed to occur in an equation set (also called unification problem), and which expressions are considered equal, several frameworks of unification are distinguished. If higher-order variables, that is, variables representing functions, are allowed in an expression, the process is called higher-order unification, otherwise first-order unification. If a solution is required to make both sides of each equation literally equal, the process is called syntactical unification, otherwise semantical, or equational unification, or E-unification, or unification modulo theory.A solution of a unification problem is denoted as a substitution, that is, a mapping assigning a symbolic value to each variable of the problem's expressions. A unification algorithm should compute for a given problem a complete, and minimal substitution set, that is, a set covering all its solutions, and containing no redundant members. Depending on the framework, a complete and minimal substitution set may have at most one, at most finitely many, or possibly infinitely many members, or may not exist at all. In some frameworks it is generally impossible to decide whether any solution exists. For first-order syntactical unification, Martelli and Montanari gave an algorithm that reports unsolvability or computes a complete and minimal singleton substitution set containing the so-called most general unifier.For example, using x,y,z as variables, the singleton equation set { cons(x,cons(x,nil)) = cons(2,y) } is a syntactic first-order unification problem that has the substitution { x ↦ 2, y ↦ cons(2,nil) } as its only solution.The syntactic first-order unification problem { y = cons(2,y) } has no solution over the set of finite terms; however, it has the single solution { y ↦ cons(2,cons(2,cons(2,...))) } over the set of infinite trees.The semantic first-order unification problem { a⋅x = x⋅a } has each substitution of the form { x ↦ a⋅...⋅a } as a solution in a semigroup, i.e. if (⋅) is considered associative; the same problem, viewed in an abelian group, where (⋅) is considered also commutative, has any substitution at all as a solution.The singleton set { a = y(x) } is a syntactic second-order unification problem, since y is a function variable.One solution is { x ↦ a, y ↦ (identity function) }; another one is { y ↦ (constant function mapping each value to a), x ↦ (any value) }.The first formal investigation of unification can be attributed to John Alan Robinson, who used first-order syntactical unification as a basic building block of his resolution procedure for first-order logic, a great step forward in automated reasoning technology, as it eliminated one source of combinatorial explosion: searching for instantiation of terms. Today, automated reasoning is still the main application area of unification.Syntactical first-order unification is used in logic programming and programming language type system implementation, especially in Hindley–Milner based type inference algorithms.Semantic unification is used in SMT solvers and term rewriting algorithms.Higher-order unification is used in proof assistants, for example Isabelle and Twelf, and restricted forms of higher-order unification (higher-order pattern unification) are used in some programming language implementations, such as lambdaProlog, as higher-order patterns are expressive, yet their associated unification procedure retains theoretical properties closer to first-order unification.
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