computer science

Solver

Solver is a computer science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Solver rather than just read about it. In short: A solver is a piece of mathematical software, possibly in the form of a stand-alone computer program or as a software library, that 'solves' a mathematical problem. A solver takes problem descriptions in some sort of generic form and calculates their solution.

Key takeaways

Solver belongs to computer science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Solver to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Solver from memory before moving on to harder problems.

Reference excerpt

A solver is a piece of mathematical software, possibly in the form of a stand-alone computer program or as a 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 and non-linear equations. In the case of a single equation, the "solver" is more appropriately called a root-finding algorithm. Systems of linear equations. Nonlinear systems. Systems of polynomial equations, which are a special case of nonlinear systems, better solved by specific solvers. Linear and non-linear optimisation problems Systems of ordinary differential equations Systems of differential algebraic equations Boolean satisfiability problems, including SAT solvers Quantified boolean formula solvers Constraint satisfaction problems Shortest path problems Minimum spanning tree problems Combinatorial optimization Game solvers for problems in game theory Three-body problem The General Problem Solver (GPS) is a particular computer program created in 1957 by Herbert Simon, 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 rules) from its strategy of how to solve problems (as a general search 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 equations) 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

Worked examples

Example 1 — a first encounter with Solver

Start with the simplest possible case. Write down what Solver claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In computer science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Solver before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Solver ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Solver

In research: Solver appears in computer science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Solver in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Solver is common in secondary-school and first-year university syllabi. It links to neighbouring topics Formal methods tools, Numerical software, so understanding it makes those chapters shorter.
In everyday life: Look for Solver outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Solver in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Solver means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Solver out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Solver in simple terms?

Why does Solver matter?

Because it connects several computer science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Solver?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Solver.