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The structured program theorem, also called the Böhm–Jacopini theorem, [1] [2] is a result in programming language theory. It states that a class of control-flow graphs (historically called flowcharts in this context) can compute any computable function if it combines subprograms in only three specific ways ( control structures ).
Structured programming is a programming paradigm aimed at improving the clarity, quality, and development time of a computer program by making specific disciplined use of the structured control flow constructs of selection (if/then/else) and repetition (while and for), block structures, and subroutines.
In mathematics, in the field of abstract algebra, the structure theorem for finitely generated modules over a principal ideal domain is a generalization of the fundamental theorem of finitely generated abelian groups and roughly states that finitely generated modules over a principal ideal domain (PID) can be uniquely decomposed in much the same way that integers have a prime factorization.
Corrado Böhm (17 January 1923 – 23 October 2017) was an Italian computer scientist and Professor Emeritus at the University of Rome "La Sapienza", known especially for his contributions to the theory of structured programming, constructive mathematics, combinatory logic, lambda calculus, and the semantics and implementation of functional programming languages.
The structured program theorem proved that the goto statement is not necessary to write programs that can be expressed as flow charts; some combination of the three programming constructs of sequence, selection/choice, and repetition/iteration are sufficient for any computation that can be performed by a Turing machine, with the caveat that ...
Section VI of McCabe's 1976 paper is concerned with determining what the control-flow graphs (CFGs) of non-structured programs look like in terms of their subgraphs, which McCabe identified. (For details, see structured program theorem.) McCabe concluded that section by proposing a numerical measure of how close to the structured programming ...
A declarative programming program describes what the problem is, not how to solve it. The program is structured as a set of properties to find in the expected result, not as a procedure to follow. Given a database or a set of rules, the computer tries to find a solution matching all the desired properties.
The Valiant–Vazirani theorem is a theorem in computational complexity theory. It was proven by Leslie Valiant and Vijay Vazirani in their paper titled NP is as easy as detecting unique solutions published in 1986. [2] The theorem states that if there is a polynomial time algorithm for Unambiguous-SAT, then NP=RP.