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Aside from his work in theoretical computer science, Savitch wrote a number of textbooks for learning to program in C/C++, Java, Ada, Pascal and others. Savitch received his PhD in mathematics from University of California, Berkeley in 1969 under the supervision of Stephen Cook .
The program in this example illustrates the "generate-and-test" organization that is often found in simple ASP programs. The choice rule describes a set of "potential solutions"—a simple superset of the set of solutions to the given search problem. It is followed by a constraint, which eliminates all potential solutions that are not acceptable.
In other words, if a nondeterministic Turing machine can solve a problem using () space, a deterministic Turing machine can solve the same problem in the square of that space bound. [1] Although it seems that nondeterminism may produce exponential gains in time (as formalized in the unproven exponential time hypothesis ), Savitch's theorem ...
A reduction is a transformation of one problem into another problem, i.e. a reduction takes inputs from one problem and transforms them into inputs of another problem. For instance, you can reduce ordinary base-10 addition x + y {\displaystyle x+y} to base-2 addition by transforming x {\displaystyle x} and y {\displaystyle y} to their base-2 ...
NP contains all problems in P, since one can verify any instance of the problem by simply ignoring the proof and solving it. NP is contained in PSPACE —to show this, it suffices to construct a PSPACE machine that loops over all proof strings and feeds each one to a polynomial-time verifier.
An alternative characterization of PSPACE is the set of problems decidable by an alternating Turing machine in polynomial time, sometimes called APTIME or just AP. [4]A logical characterization of PSPACE from descriptive complexity theory is that it is the set of problems expressible in second-order logic with the addition of a transitive closure operator.
Given a real vector space X, a convex, real-valued function: defined on a convex cone, and an affine subspace defined by a set of affine constraints () = , a conic optimization problem is to find the point in for which the number () is smallest.
In computer science and mathematical logic, satisfiability modulo theories (SMT) is the problem of determining whether a mathematical formula is satisfiable.It generalizes the Boolean satisfiability problem (SAT) to more complex formulas involving real numbers, integers, and/or various data structures such as lists, arrays, bit vectors, and strings.