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The Identity Correspondence Problem (ICP) asks whether a finite set of pairs of words (over a group alphabet) can generate an identity pair by a sequence of concatenations. The problem is undecidable and equivalent to the following Group Problem: is the semigroup generated by a finite set of pairs of words (over a group alphabet) a group. [11]
For every long enough string in a regular language, there must be a middle section that can be repeated (or pumped) any number of times to produce a string still in the language. In the theory of formal languages, the pumping lemma for regular languages is a lemma that describes an essential property of all regular languages.
The following phrases come from a portable media player's seven-segment display. They give a good illustration of an application where a seven-segment display may be sufficient for displaying letters, since the relevant messages are neither critical nor in any significant risk of being misunderstood, much due to the limited number and rigid domain specificity of the messages.
Sample Code: An illustration of how the pattern can be used in a programming language. Known Uses: Examples of real usages of the pattern. Related Patterns: Other patterns that have some relationship with the pattern; discussion of the differences between the pattern and similar patterns.
The C++ programming language (originally named "C with Classes") was devised by Bjarne Stroustrup as an approach to providing object-oriented functionality with a C-like syntax. [67] C++ adds greater typing strength, scoping, and other tools useful in object-oriented programming, and permits generic programming via templates.
The indirection pattern supports low coupling and reuses potential between two elements by assigning the responsibility of mediation between them to an intermediate object. An example of this is the introduction of a controller component for mediation between data (model) and its representation (view) in the model-view-controller pattern.
For example, the language L p of even-length palindromes on the alphabet of 0 and 1 has the context-free grammar S → 0S0 | 1S1 | ε. If a DPDA for this language exists, and it sees a string 0 n, it must use its stack to memorize the length n, in order to be able to distinguish its possible continuations 0 n 11 0 n ∈ L p and 0 n 11 0 n+2 ∉ ...
This pattern is used to avoid subclasses of an object creator in the client application, like the factory method pattern does, and to avoid the inherent cost of creating a new object in the standard way (e.g., using the 'new' keyword) when it is prohibitively expensive for a given application.