About: Parsimonious reduction

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In computational complexity theory and game complexity, a parsimonious reduction is a transformation from one problem to another (a reduction) that preserves the number of solutions. Informally, it is a bijection between the respective sets of solutions of two problems. A general reduction from problem to problem is a transformation that guarantees that whenever has a solution also has at least one solution and vice versa. A parsimonious reduction guarantees that for every solution of , there exists a unique solution of and vice versa.

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  • In computational complexity theory and game complexity, a parsimonious reduction is a transformation from one problem to another (a reduction) that preserves the number of solutions. Informally, it is a bijection between the respective sets of solutions of two problems. A general reduction from problem to problem is a transformation that guarantees that whenever has a solution also has at least one solution and vice versa. A parsimonious reduction guarantees that for every solution of , there exists a unique solution of and vice versa. Parsimonious reductions are commonly used in computational complexity for proving the hardness of counting problems, for counting complexity classes such as #P. Additionally, they are used in game complexity, as a way to design hard puzzles that have a unique solution, as many types of puzzles require. (en)
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  • In computational complexity theory and game complexity, a parsimonious reduction is a transformation from one problem to another (a reduction) that preserves the number of solutions. Informally, it is a bijection between the respective sets of solutions of two problems. A general reduction from problem to problem is a transformation that guarantees that whenever has a solution also has at least one solution and vice versa. A parsimonious reduction guarantees that for every solution of , there exists a unique solution of and vice versa. (en)
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  • Parsimonious reduction (en)
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