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Informally, an algorithm is a set of explicit instructions used to solve a problem (e.g. Euclid's algorithm for computing the greatest common divisor of two integers). For more specific questions on algorithms, this tag may be used in conjunction with the approximation-algorithms, algorithmic-randomness and algorithmic-topology tags.
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Algorithms to factorize words into product of powers
Let $A$ be a finite set of symbols, are there efficient algorithms that take as input a word $w$ over $A$ and return as output a representation of $w$ in terms of product of powers? … Of course, this representation is not unique, for example for $A = \{0,1\}$ we have
$$0101010010010 = (01)^3 (001)^2 0 = (01)^2 (010)^3 ,$$
so they might be algorithms that impose further restrictions …