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The procedure is based on unit clauses, i.e. clauses that are composed of a single literal, in conjunctive normal form. Because each clause needs to be satisfied, we know that this literal must be true. If a set of clauses contains the unit clause , the other clauses are simplified by the application of the two following rules:
Element in X[row 2; col 2] is changed (from 7) to a nested vector "Text" using the enclose ⊂ function. Element in X[row 3; col 4], formerly integer 14, now becomes a mini enclosed or ⊂ nested 2x2 matrix of 4 consecutive integers. Since X contains numbers, text and nested elements, it is both a mixed and a nested array.
The authors demonstrate a proof that any Boolean (logic) function can be expressed in either disjunctive or conjunctive normal form (cf pages 5–6); the proof simply proceeds by creating all 2 N rows of N Boolean variables and demonstrates that each row ("minterm" or "maxterm") has a unique Boolean expression.
Wirth syntax notation (WSN) is a metasyntax, that is, a formal way to describe formal languages.Originally proposed by Niklaus Wirth in 1977 as an alternative to Backus–Naur form (BNF).
In computer science, a literal is a textual representation (notation) of a value as it is written in source code. [1] [2] Almost all programming languages have notations for atomic values such as integers, floating-point numbers, and strings, and usually for Booleans and characters; some also have notations for elements of enumerated types and compound values such as arrays, records, and objects.
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The idea of their solution is to guess the indexes of rows containing the leftmost and rightmost cells of the shape to be reconstructed, and then to set up a 2-satisfiability problem that tests whether there exists a shape consistent with these guesses and with the given row and column sums. They use four 2-satisfiability variables for each ...
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