This chapter discusses how to specify various Latin squares so that their existence can be eeciently decided by computer programs. The computer programs considered here are so-called general-purpose model generation programs (or simply model generators) that are used to solve constraint satisfaction problems in AI, to prove theorems in nite domains, or to produce counterexamples to false conjec...

Among many variations of pencil puzzles, Latin square Completion-Type puzzles (LSCP), such as Sudoku, Futoshiki and BlockSum, are quite popular for puzzle fans. Concerning these puzzles, the solvability has been investigated from the viewpoint of time complexity in the last decade; it has been shown that, in most of these puzzles, it is NP-complete to determine whether a given puzzle instance h...

Optical network uses a tool for routing called Latin router. These routers use particular algorithms for routing. For example, we can refer to LDF algorithm that uses backtracking (one of CSP methods) for problem solving. In this paper, we proposed new approached for completion routing table (DRA&CRA algorithm) and compare with pervious proposed ways and showed numbers of backtracking, blocking...

A class of Balanced Bipartite Row-Column Designs (BBPRC-designs) in two sets of treatments of sizes v1=v and v2=v+1 with replications 2(v-1) and 2v, respectively, has been constructed by replacing the ii-th positions of 2v × 2v standard cyclic latin square design in 2v treatments by 2v treatments by (2v+1)-th treatment. Such design finds applications in agricultural and industrial experimentati...

Keywords: Self-orthogonal Latin square Strongly symmetric Magic square Yang Hui type a b s t r a c t In this paper, a strongly symmetric self-orthogonal diagonal Latin square of order n with a special property (* SSSODLS(n)) is introduced. It is proved that a * SSSODLS(n) exists if and only if n ≡ 0 (mod 4) and n ̸ = 4. As an application, it is shown that there exists a Yang Hui type magic squar...

The Latin Square Task (LST) was proposed as a theoretically well-grounded paradigm for measuring fluid intelligence. In four studies (total N = 3,439) we systematically investigated the psychometric properties of LSTs. Results provided evidence that (a) construct is unidimensional, (b) administered stimulus types and rotation item matrix only played minor role, (c) relations with other measures...