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.
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complexity theory and game complexity, a parsimoniousreduction is a transformation from one problem to another (a reduction) that preserves the number of solutions...
NP-complete. This can be proved either by a many-one reduction from 3-satisfiability, or by a parsimoniousreduction from the closely related Hamiltonian path problem...
Nagao, Tadaaki (1996), NP-completeness results for NONOGRAM via ParsimoniousReductions, vol. TR96-0008, Technical Report, Department of Computer Science...
has a reduction to it, it must be NP-complete. It is also possible to prove more strongly that there exists an invertible parsimoniousreduction to the...
intractable; it is #P-hard. In fact, this problem is complete (under parsimoniousreductions) for the complexity class SpanL. NFAs and DFAs are equivalent in...
#P-complete because the decision problem is known to be NP-complete via a parsimoniousreduction. The question which points admit a good approximation algorithm...
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its modes are not orthogonal, DMD-based representations can be less parsimonious than those generated by PCA. However, they can also be more physically...
autocovariance operator. FPCA represents functional data in the most parsimonious way, in the sense that when using a fixed number of basis functions,...
basis of whether it is "accurate", "consistent", "has broad scope", "parsimonious", and "fruitful". Karl Popper (1934) Logik der Forschung, rewritten in...
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a machine learning technique that uses Bayesian inference to obtain parsimonious solutions for regression and probabilistic classification. The RVM has...
suggested that overtreatment can also be understood in contrast to 'parsimonious care', defined as "care that utilizes the most efficient means to effectively...
of Thalattosuchia is the most parsimonious result, this may change as more species are described. The most parsimonious trees of either analysis are shown...
actually a distinct integument unrelated to origin of feathers. The most parsimonious scenario is the presence of feathers in the last common ancestor of pterosaurs...
unweighted networks. Therefore, weighted (correlation) networks allow for a parsimonious parametrization (in terms of modules and module membership) (chapters...
hypothetically placed this species in the Indian clade because it is the most parsimonious solution regarding the biogeography of anemonefish species. Society,...
historian W.R.W. Stephens, "affords some illustrations of the avaricious and parsimonious character of the king". It seems that Henry was skilful at extracting...
occasionally been reused for a useful purpose, which is expected for parsimonious lithic resource exploitation A microburin is a fragment of a lithic flake...
parameter optimization. It is used to efficiently and effectively produce a parsimonious RBF neural network that generalizes well. It is achieved through simultaneous...
Jeholornis. This suggests a non-hypercarnivorous lifestyle to be a more parsimonious conclusion and supports Cau's initial interpretations of its specializations...
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