# Glossary¶

This page is in very early stage of writing. It's most prominent feature is its incompleteness.

## accessible (or reachable, or initially connected)¶

A state $s$ is accessible if there is a path from an initial state to $s$.

An automaton is /accessible/ if all its states are.

See:

## Antimirov automaton¶

See derived-term automaton.

## derived-term automaton¶

See *expression*.derived_term.

## equation automaton¶

See derived-term automaton.

## has_lightening_cycle¶

A lightening cycle is a path from a state to itself that is either negative (for $\mathbb{Q}$, $\mathbb{R}$ and $\mathbb{Z}$), or between 0 and 1 (for $\mathbb{Q}$, $\mathbb{R}$ and $\mathbb{R}_\text{min}$).

## is_commutative¶

A valueset is commutative if `mul(u, v) == mul(v, u)`

.

## is_free¶

A labelset is free if the labels are only "letters". This is a requirement for algorithms such as `determinize`

, `evaluate`

.

`letterset`

is free.
`nullableset`

is not free.
`oneset`

is not free.
`wordset`

is not free.
`tupleset`

is free if its components are free.

If the labelset is free, then `label_t`

is `letter_t`

.

## is_idempotent¶

A valueset is idempotent if `add(v, v) == v`

.

## is_letterized¶

A labelset is letterized if it free, or nullable of free. In other words, its labels are either letters, or the empty word. Maybe surprisingly, oneset ($\{1\}$) is letterized.

## partial-derivative automaton¶

See derived-term automaton.

## position automaton¶

See standard automaton.