Formal language in computational complexity theory
In computational complexity theory, a unary language or tally language is a formal language (a set of strings) where all strings have the form 1k, where "1" can be any fixed symbol. For example, the language {1, 111, 1111} is unary, as is the language {1k | k is prime}. The complexity class of all such languages is sometimes called TALLY.
The name "unary" comes from the fact that a unary language is the encoding of a set of natural numbers in the unary numeral system. Since the universe of strings over any finite alphabet is a countable set, every language can be mapped to a unique set A of natural numbers; thus, every language has a unary version {1k | k in A}. Conversely, every unary language has a more compact binary version, the set of binary encodings of natural numbers k such that 1k is in the language.
Since complexity is usually measured in terms of the length of the input string, the unary version of a language can be "easier" than the original language. For example, if a language can be recognized in O(2n) time, its unary version can be recognized in O(n) time, because n has become exponentially larger. More generally, if a language can be recognized in O(f(n)) time and O(g(n)) space, its unary version can be recognized in O(n + f(log n)) time and O(g(log n)) space (we require O(n) time just to read the input string). However, if membership in a language is undecidable, then membership in its unary version is also undecidable.
In computational complexity theory, a unarylanguage or tally language is a formal language (a set of strings) where all strings have the form 1k, where...
In mathematics, a unary operation is an operation with only one operand, i.e. a single input. This is in contrast to binary operations, which use two...
The unary numeral system is the simplest numeral system to represent natural numbers: to represent a number N, a symbol representing 1 is repeated N times...
In mathematics, a unary function is a function that takes one argument. A unary operator belongs to a subset of unary functions, in that its codomain...
concatenation operations. Later, Jeż showed that non-regular unarylanguages can be defined by language equations with union, intersection and concatenation,...
Unary coding, or the unary numeral system and also sometimes called thermometer code, is an entropy encoding that represents a natural number, n, with...
football club Tally (cap), a ribbon on a sailor's cap Tally language, a form of unarylanguage in computational complexity theory Tally light, a small signal-lamp...
predicate symbols can be unary, binary or of higher arities. The finite set of predicate symbols may vary while the rest of the language is fixed. It is a convention...
unarylanguage. The non-emptiness problem (is the language of an input AFA non-empty?), the universality problem (is the complement of the language of...
contains rapidly goes to zero as n grows. All unarylanguages are sparse. An example of a nontrivial sparse language is the set of binary strings containing...
the returned value, the result is undefined. GCC extends the C language with a unary && operator that returns the address of a label. This address can...
computation and genetic programming. The PORS language consists of two terminal nodes (1 and recall), one unary operation (store) and one binary operation...
of unary operators in mathematics and in programming include the unary minus and plus, the increment and decrement operators in C-style languages (not...
every unarylanguage. From a descriptive complexity viewpoint, DLOGTIME-uniform AC0 is equal to the descriptive class FO+BIT of all languages describable...
and programming languages, notably Microsoft Excel, PlanMaker (and other spreadsheet applications) and the programming language bc, unary operations have...
operator The binary - operator always casts both operands to a number Both unary operators (+, -) always cast the operand to a number Values are cast to...
{\displaystyle \nleftrightarrow } , ⊥, ⊄, ⊅ (see validity). Involutivity (for unary connectives) f(f(a)) = a. E.g. negation in classical logic. For classical...
aRatherBigNumber := 42 factorial "factorial" above is what is called a unary message because only one object, the receiver, is involved. Messages can...
are unary operators that increase or decrease their operand by one. They are commonly found in imperative programming languages. C-like languages feature...
standard ICs such as the CMOS 4511. A binary to unary decoder converts each binary value to its associated unary representation. Unlike the 1-of-n (one-hot)...
identifies a unarylanguage, or tally language, which is in one class but not the other. In the original theorem, the separating language was arbitrary...
qf, 1, stay). This machine performs incrementation by one of a number in unary encoding: It loops over any number of "1" cells and appends an additional...
computer science, the Kleene star (or Kleene operator or Kleene closure) is a unary operation, either on sets of strings or on sets of symbols or characters...
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