Glossary

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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.