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Metamorphic testing (MT) is a property-based software testing technique, which can be an effective approach for addressing the test oracle problem and test case generation problem. The test oracle problem is the difficulty of determining the expected outcomes of selected test cases or to determine whether the actual outputs agree with the ...
An oracle machine can perform all of the usual operations of a Turing machine, and can also query the oracle to obtain a solution to any instance of the computational problem for that oracle. For example, if the problem is a decision problem for a set A of natural numbers, the oracle machine supplies the oracle with a natural number, and the ...
A rank oracle takes as its input a set of matroid elements, and returns as its output a numerical value, the rank of the given set. [ 9 ] Three types of closure oracle have been considered: one that tests if a given element belongs to the closure of a given set, a second one that returns the closure of the set, and a third one that tests ...
In other words, if a language is defined based on some oracle in C, then we can assume that it is defined based on a complete problem for C. Complete problems therefore act as "representatives" of the class for which they are complete. The Sipser–Lautemann theorem states that the class BPP is contained in the second level of the polynomial ...
A specified oracle is typically associated with formalized approaches to software modeling and software code construction. It is connected to formal specification, [8] model-based design which may be used to generate test oracles, [9] state transition specification for which oracles can be derived to aid model-based testing [10] and protocol conformance testing, [11] and design by contract for ...
In mathematical optimization, oracle complexity is a standard theoretical framework to study the computational requirements for solving classes of optimization problems. It is suitable for analyzing iterative algorithms which proceed by computing local information about the objective function at various points (such as the function's value, gradient, Hessian etc.).
Finite-rank operators are matrices (of finite size) transplanted to the infinite dimensional setting. As such, these operators may be described via linear algebra techniques. From linear algebra, we know that a rectangular matrix, with complex entries, M ∈ C n × m {\displaystyle M\in \mathbb {C} ^{n\times m}} has rank 1 {\displaystyle 1} if ...
The problem can be presented as an LP with a constraint for each subset of vertices, which is an exponential number of constraints. However, a separation oracle can be implemented using n-1 applications of the minimum cut procedure. [3] The maximum independent set problem. It can be approximated by an LP with a constraint for every odd-length ...