Solver
 | This articleneeds additional citations forverification.(September 2009) |
Asolveris a piece ofmathematical software,possibly in the form of a stand-alonecomputer programor as asoftware library,that 'solves' a mathematical problem. A solver takes problem descriptions in some sort of generic form and calculates their solution. In a solver, the emphasis is on creating a program or library that can easily be applied to other problems of similar type.
Solver types[edit]
Types of problems with existing dedicated solvers include:
- Linearandnon-linear equations.In the case of a single equation, the "solver" is more appropriately called aroot-finding algorithm.
- Systems of linear equations.
- Nonlinear systems.
- Systems of polynomial equations,which are a special case of non linear systems, better solved by specific solvers.
- Linear and non-linearoptimisationproblems
- Systems ofordinary differential equations
- Systems ofdifferential algebraic equations
- Boolean satisfiability problems,includingSAT solvers
- Quantified boolean formulasolvers[1]
- Constraint satisfaction problems
- Shortest path problems
- Minimum spanning treeproblems
- Combinatorial optimization[2]
- Game solversfor problems ingame theory[3]
- Three-body problem[4]
TheGeneral Problem Solver(GPS) is a particular computer program created in 1957 byHerbert Simon,J. C. Shaw,andAllen Newellintended to work as a universal problem solver, that theoretically can be used to solve every possible problem that can be formalized in a symbolic system, given the right input configuration. It was the first computer program that separated its knowledge of problems (in the form ofdomainrules) from its strategy of how to solve problems (as a general searchengine).
General solvers typically use an architecture similar to the GPS to decouple a problem's definition from the strategy used to solve it. The advantage in this decoupling is that the solver does not depend on the details of any particular problem instance. The strategy utilized by general solvers was based on a general algorithm (generally based onbacktracking) with the only goal of completeness. This induces an exponentialcomputational timethat dramatically limits their usability. Modern solvers use a more specialized approach that takes advantage of the structure of the problems so that the solver spends as little time as possible backtracking.
For problems of a particular class (e.g., systems ofnon-linear equations) multiple algorithms are usually available. Some solvers implement multiple algorithms.
See also[edit]
- Mathematical softwarefor other types of mathematical software.
- Problem solving environment:a specialized software combining automated problem-solving methods with human-oriented tools for guiding the problem resolution.
- Satisfiability modulo theoriesfor solvers of logical formulas with respect to combinations of background theories expressed in classical first-order logic with equality.
- Semantic reasoner
Lists of solvers[edit]
- List of linear programming solvers
- List of SMT solvers
- List of solvers for ordinary differential equations
References[edit]
- ^Using QBF Solvers to Solve Games and Puzzles- Boston College
- ^Zhang, Weixiong (2012-12-06).State-Space Search: Algorithms, Complexity, Extensions, and Applications.Springer Science & Business Media.ISBN978-1-4612-1538-7.
- ^Bowling, Michael, and Manuela Veloso.An analysis of stochastic game theory for multiagent reinforcement learning.No. CMU-CS-00-165. Carnegie-Mellon Univ Pittsburgh Pa School of Computer Science, 2000.
- ^"A neural net solves the three-body problem 100 million times faster".MIT Technology Review.October 26, 2019.Retrieved2021-05-16.