In mathematics, in the field of tropical analysis, the log semiring is the semiring structure on the logarithmic scale, obtained by considering the extended...

semiring called the trivial semiring. This triviality can be characterized via 0 = 1 {\displaystyle 0=1} and so when speaking of nontrivial semirings...

In idempotent analysis, the tropical semiring is a semiring of extended real numbers with the operations of minimum (or maximum) and addition replacing...

and form a semiring, called the probability semiring; this is in fact a semifield. The logarithm then takes multiplication to addition (log multiplication)...

family. In tropical analysis, this is the sum in the log semiring. Logarithmic mean Log semiring Smooth maximum Softmax function Zhang, Aston; Lipton...

Napier Level (logarithmic quantity) Log–log plot Logarithm Logarithmic mean Log semiring Preferred number Semi-log plot Order of magnitude Entropy Entropy...

relates log semiring to the min-plus semiring. lim T → 0 − T log ⁡ ( e − s T + e − t T ) = m i n { s , t } {\displaystyle \lim _{T\rightarrow 0}-T\log(e^{-{\frac...

extended by an absorbing 0, forming the probability semiring, which is isomorphic to the log semiring. Rational functions of the form f /g, where f and...

arg min, corresponding to using the log semiring instead of the max-plus semiring (respectively min-plus semiring), and recovering the arg max or arg...

f(x)=\exp(x)} , then the f-mean is the mean in the log semiring, which is a constant shifted version of the LogSumExp (LSE) function (which is the logarithmic...

Extended complex plane Extended natural numbers Improper integral Infinity Log semiring Series (mathematics) Projectively extended real line Computer representations...

the set of weights to form a semiring. Two typical semirings used in practice are the log semiring and tropical semiring: nondeterministic automata may...

case of the Stolarsky mean. Logarithmic mean temperature difference Log semiring Citations B. C. Carlson (1966). "Some inequalities for hypergeometric...

{\displaystyle \mathbb {R} _{\geq 0}} has a semiring structure (0 being the additive identity), known as the probability semiring; taking logarithms (with a choice...

instead. aProbLog generalizes ProbLog by allowing any commutative semiring instead of just probabilities. ProbFOIL: given a set of ProbLog facts as a probabilistic...

semiring. This is defined in two ways, depending on max or min convention. The min tropical semiring T {\displaystyle \mathbb {T} } is the semiring T...

approach to these is to consider the two operations to be those of a semiring. Semiring multiplication is done along the path, and the addition is between...

addition form a semiring, called the min tropical semiring, and a valuation v is almost a semiring homomorphism from K to the tropical semiring, except that...

requires that the entries belong to a semiring, and does not require multiplication of elements of the semiring to be commutative. In many applications...

near-semiring, and some additive monads do qualify as such. However, not all additive monads meet the distributive laws of even a near-semiring. In Haskell...

Magnus ring over R. Given an alphabet Σ {\displaystyle \Sigma } and a semiring S {\displaystyle S} . The formal power series over S {\displaystyle S}...

Strassen's algorithm works for any ring, such as plus/multiply, but not all semirings, such as min-plus or boolean algebra, where the naive algorithm still...

a regular expression, with the difference being the use of a min-plus semiring. The modern formulation of the algorithm as three nested for-loops was...

problem to graphs with edges weighted by the elements of an (arbitrary) semiring.[jargon] An example of an accepting state appears in Fig. 5: a deterministic...

generalization, this time in the context of a formal power series over a semiring. This approach gives rise to weighted rational expressions and weighted...

magma (M, •) to (N, ∗). proof: log ⁡ x y   =   log ⁡ x + log ⁡ y 2 {\displaystyle \log {\sqrt {xy}}\ =\ {\frac {\log x+\log y}{2}}} Note that these commutative...

lower bound for the quantity | β 1 log ⁡ α 1 + β 2 log ⁡ α 2 | {\displaystyle |\beta _{1}\log \alpha _{1}+\beta _{2}\log \alpha _{2}|\,} where all four unknowns...

is valid more generally for two elements x and y in a ring, or even a semiring, provided that xy = yx. For example, it holds for two n × n matrices, provided...

automaton A is unambiguous, then the set of weight does not need to be a semiring, instead it suffices to consider a monoid. Indeed, there is at most one...

over the unary alphabet Σ = { a } {\displaystyle \Sigma =\{a\}} over the semiring ( R , + , × ) {\displaystyle (\mathbb {R} ,+,\times )} (which is in fact...