Practical Decision
Having practical decision procedures for classes of logical formulas is of considerable interest for program verification and circuit verification. Pure Boolean logical formulas are usually decided using SAT-solving techniques based on the DPLL algorithm. Conjunctive formulas over linear real or rational arithmetic can be decided using the simplex algorithm, formulas in linear integer arithmetic (Presburger arithmetic) can be decided using Cooper's algorithm or William Pugh's Omega test. Formulas with negations, conjunctions and disjunctions combine the difficulties of satisfiability testing with that of decision of conjunctions; they are generally decided nowadays using SMT-solving technique, which combine SAT-solving with decision procedures for conjunctions and propagation techniques. Real polynomial arithmetic, also known as the theory of real closed fields, is decidable, for instance using the cylindrical algebraic decomposition; unfortunately the complexity of that algorithm is excessive for most practical uses.
A leading scientific conference in this field is Computer Aided Verification.
Read more about this topic: Decision Problem
Famous quotes containing the words practical and/or decision:
“[Girls] study under the paralyzing idea that their acquirements cannot be brought into practical use. They may subserve the purposes of promoting individual domestic pleasure and social enjoyment in conversation, but what are they in comparison with the grand stimulation of independence and self- reliance, of the capability of contributing to the comfort and happiness of those whom they love as their own souls?”
—Sarah M. Grimke (1792–1873)
“A good decision is based on knowledge and not on numbers.”
—Plato (c. 427–347 B.C.)