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:
“Great statesmen seem to direct and rule by a sort of power to put themselves in the place of the nation over which they are set, and may thus be said to possess the souls of poets at the same time they display the coarser sense and the more vulgar sagacity of practical men of business.”
—Woodrow Wilson (1856–1924)
“The decision to have a child is both a private and a public decision, for children are our collective future.”
—Sylvia Ann Hewitt (20th century)