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Combinatory logic is a notation to eliminate the need for quantified variables in mathematical logic.It was introduced by Moses Schönfinkel [1] and Haskell Curry, [2] and has more recently been used in computer science as a theoretical model of computation and also as a basis for the design of functional programming languages.
Historically, dead-code elimination was performed using information derived from data-flow analysis. [3] An algorithm based on static single-assignment form (SSA) appears in the original journal article on SSA form by Ron Cytron et al. [ 4 ] Robert Shillingsburg (aka Shillner) improved on the algorithm and developed a companion algorithm for ...
Fourier–Motzkin elimination, also known as the FME method, is a mathematical algorithm for eliminating variables from a system of linear inequalities. It can output real solutions. The algorithm is named after Joseph Fourier [ 1 ] who proposed the method in 1826 and Theodore Motzkin who re-discovered it in 1936.
The bucket elimination algorithm can be adapted for constraint optimization. A given variable can be indeed removed from the problem by replacing all soft constraints containing it with a new soft constraint. The cost of this new constraint is computed assuming a maximal value for every value of the removed variable.
A variant of the 3-satisfiability problem is the one-in-three 3-SAT (also known variously as 1-in-3-SAT and exactly-1 3-SAT). Given a conjunctive normal form with three literals per clause, the problem is to determine whether there exists a truth assignment to the variables so that each clause has exactly one TRUE literal (and thus exactly two ...
In contrast to linear programming, which can be solved efficiently in the worst case, integer programming problems are in many practical situations (those with bounded variables) NP-hard. 0–1 integer programming or binary integer programming (BIP) is the special case of integer programming where variables are required to be 0 or 1 (rather ...
The resulting information can be used in optimizations such as redundancy elimination, dead code elimination, instruction selection, etc., but can also be used to improve the safety of programs, e.g. in the detection of buffer overruns. [2] Techniques for value range analysis typically use symbolic analysis extensively. [3]
code which is executed but has no external effect (e.g., does not change the output produced by a program; known as dead code). A NOP instruction might be considered to be redundant code that has been explicitly inserted to pad out the instruction stream or introduce a time delay, for example to create a timing loop by "wasting time".