BPP (complexity)In computational complexity theory, a branch of computer science, bounded-error probabilistic polynomial time (BPP) is the class of decision problems solvable by a probabilistic Turing machine in polynomial time with an error probability bounded by 1/3 for all instances. BPP is one of the largest practical classes of problems, meaning most problems of interest in BPP have efficient probabilistic algorithms that can be run quickly on real modern machines.
Criminal procedureCriminal procedure is the adjudication process of the criminal law. While criminal procedure differs dramatically by jurisdiction, the process generally begins with a formal criminal charge with the person on trial either being free on bail or incarcerated, and results in the conviction or acquittal of the defendant. Criminal procedure can be either in form of inquisitorial or adversarial criminal procedure.
Communication complexityIn theoretical computer science, communication complexity studies the amount of communication required to solve a problem when the input to the problem is distributed among two or more parties. The study of communication complexity was first introduced by Andrew Yao in 1979, while studying the problem of computation distributed among several machines. The problem is usually stated as follows: two parties (traditionally called Alice and Bob) each receive a (potentially different) -bit string and .
Civil procedureCivil procedure is the body of law that sets out the rules and standards that courts follow when adjudicating civil lawsuits (as opposed to procedures in criminal law matters). These rules govern how a lawsuit or case may be commenced; what kind of service of process (if any) is required; the types of pleadings or statements of case, motions or applications, and orders allowed in civil cases; the timing and manner of depositions and discovery or disclosure; the conduct of trials; the process for judgment; the process for post-trial procedures; various available remedies; and how the courts and clerks must function.
Circuit complexityIn theoretical computer science, circuit complexity is a branch of computational complexity theory in which Boolean functions are classified according to the size or depth of the Boolean circuits that compute them. A related notion is the circuit complexity of a recursive language that is decided by a uniform family of circuits (see below). Proving lower bounds on size of Boolean circuits computing explicit Boolean functions is a popular approach to separating complexity classes.
Spectral theoremIn mathematics, particularly linear algebra and functional analysis, a spectral theorem is a result about when a linear operator or matrix can be diagonalized (that is, represented as a diagonal matrix in some basis). This is extremely useful because computations involving a diagonalizable matrix can often be reduced to much simpler computations involving the corresponding diagonal matrix. The concept of diagonalization is relatively straightforward for operators on finite-dimensional vector spaces but requires some modification for operators on infinite-dimensional spaces.
