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{{Short description|Software for a class of mathematical problems}}
{{For|the band|Solver (band)}}
{{more citations needed|date=September 2009}}
A '''solver''' is a piece of [[mathematical software]], possibly in the form of a stand-alone [[computer program]] or as a [[Library (computing)|software 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 ==
Types of problems with existing dedicated solvers include:

* [[Linear equation|Linear]] and [[non-linear equation]]s. In the case of a single equation, the "solver" is more appropriately called a [[root-finding algorithm]].
* [[System of linear equations|Systems of linear equations]].
* [[Nonlinear system]]s.
* [[Systems of polynomial equations]], which are a special case of non linear systems, better solved by specific solvers.
* Linear and non-linear [[Optimization (mathematics)|optimisation]] problems
* Systems of [[ordinary differential equation]]s
* Systems of [[differential algebraic equation]]s
* [[Boolean satisfiability problem]]s, including [[SAT solver]]s
* [[Quantified boolean formula]] solvers<ref>[https://www.bc.edu/content/dam/bc1/schools/mcas/cs/pdf/honors-thesis/sample5.pdf Using QBF Solvers to Solve Games and Puzzles] - Boston College</ref>
* [[Constraint satisfaction problem]]s
* [[Shortest path problem]]s
* [[Minimum spanning tree]] problems
* [[Combinatorial optimization]]<ref>{{Cite book |last=Zhang |first=Weixiong |url=https://books.google.com/books?id=dYvbBwAAQBAJ |title=State-Space Search: Algorithms, Complexity, Extensions, and Applications |date=2012-12-06 |publisher=Springer Science & Business Media |isbn=978-1-4612-1538-7 |language=en}}</ref>
* ''Game solvers'' for problems in [[game theory]]<ref>Bowling, Michael, and Manuela Veloso. [https://apps.dtic.mil/dtic/tr/fulltext/u2/a385122.pdf 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.</ref>
*[[Three-body problem]]<ref>{{Cite web|date=October 26, 2019|title=A neural net solves the three-body problem 100 million times faster|url=https://www.technologyreview.com/2019/10/26/132171/a-neural-net-solves-the-three-body-problem-100-million-times-faster/|access-date=2021-05-16|website=MIT Technology Review|language=en}}</ref>

The [[General Problem Solver]] (''GPS'') is a particular computer program created in 1957 by [[Herbert A. Simon|Herbert Simon]], [[Cliff Shaw|J. C. Shaw]], and [[Allen Newell]] intended 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 of [[domain (software engineering)|domain]] rules) from its strategy of how to solve problems (as a general search [[Software engine|engine]]).

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 on [[backtracking]]) with the only goal of completeness. This induces an exponential [[computational time]] that 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 of [[non-linear equation]]s) multiple algorithms are usually available. Some solvers implement multiple algorithms.

==See also==
* [[Mathematical software]] for 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 theories]] for solvers of logical formulas with respect to combinations of background theories expressed in classical first-order logic with equality.
* [[Semantic reasoner]]

=== Lists of solvers ===
* [[List of linear programming solvers]]
* [[List of SMT solvers]]
* [[List of solvers for ordinary differential equations]]

==References==
{{Reflist}}{{Industrial and applied mathematics}}{{DEFAULTSORT:Solver (Computer Science)}}
[[Category:Numerical software]]
[[Category:Formal methods tools]]

Solver - Revision history

imported>Jarble: adding Template:Industrial and applied mathematics