Definition, Meaning & Synonyms | English word SOLVABLE

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Definitions of SOLVABLE

1. Capable of being solved.
2. (obsolete) Capable of being dissolved or liquefied.
3. (obsolete) Able to pay one's debts.
4. (obsolete, rare) Capable of being paid and discharged.

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Examples of Using SOLVABLE in a Sentence

• In computational complexity theory, bounded-error quantum polynomial time (BQP) is the class of decision problems solvable by a quantum computer in polynomial time, with an error probability of at most 1/3 for all instances.
• A computation problem is solvable by mechanical application of mathematical steps, such as an algorithm.
• While still in his teens, he was able to determine a necessary and sufficient condition for a polynomial to be solvable by radicals, thereby solving a problem that had been open for 350 years.
• This allowed him to characterize the polynomial equations that are solvable by radicals in terms of properties of the permutation group of their roots—an equation is by definition solvable by radicals if its roots may be expressed by a formula involving only integers, th roots, and the four basic arithmetic operations.
• Perturbation theory develops an expression for the desired solution in terms of a formal power series known as a perturbation series in some "small" parameter, that quantifies the deviation from the exactly solvable problem.
• In mathematics, more specifically in the field of group theory, a solvable group or soluble group is a group that can be constructed from abelian groups using extensions.
• It is possible for a system of two equations and two unknowns to have no solution (if the two lines are parallel), or for a system of three equations and two unknowns to be solvable (if the three lines intersect at a single point).
• This problem, the T-join problem, is also solvable in polynomial time by the same approach that solves the postman problem.
• The left-hand class involves little o notation, referring to the set of decision problems solvable in asymptotically less than f(n) time.
• certain semidirect products, for instance Jet groups, or some solvable groups such as that of invertible triangular matrices.
• In complexity theory, UP (unambiguous non-deterministic polynomial-time) is the complexity class of decision problems solvable in polynomial time on an unambiguous Turing machine with at most one accepting path for each input.
• Burnside's theorem in group theory states that if G is a finite group of order pq, where p and q are prime numbers, and a and b are non-negative integers, then G is solvable.
• This is generalized by Lie's theorem, which shows that any representation of a solvable Lie algebra is simultaneously upper triangularizable, the case of commuting matrices being the abelian Lie algebra case, abelian being a fortiori solvable.
• Galois theory, named after Évariste Galois, showed that some equations of at least degree 5 do not even have an idiosyncratic solution in radicals, and gave criteria for deciding if an equation is in fact solvable using radicals.
• Hartree–Fock approximation is an instance of mean-field theory, where neglecting higher-order fluctuations in order parameter allows interaction terms to be replaced with quadratic terms, obtaining exactly solvable Hamiltonians.
• The complexity class, Nick's Class (NC), of problems quickly solvable on a parallel computer, was named by Stephen Cook after Nick Pippenger for his research on circuits with polylogarithmic depth and polynomial size.
• Random instances undergo a sharp phase transition from solvable to unsolvable instances as the ratio of constraints to variables increases past 1, a phenomenon conjectured but unproven for more complicated forms of the satisfiability problem.
• In the theory of algebraic groups, a Borel subgroup of an algebraic group G is a maximal Zariski closed and connected solvable algebraic subgroup.
• While the S-matrix may be defined for any background (spacetime) that is asymptotically solvable and has no event horizons, it has a simple form in the case of the Minkowski space.
• For finitely generated linear groups, however, the von Neumann conjecture is true by the Tits alternative: every subgroup of GL(n,k) with k a field either has a normal solvable subgroup of finite index (and therefore is amenable) or contains the free group on two generators.

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