package fix

  1. Overview
  2. Docs

Module Minimize.MinimizeSource

The functor application Minimize(Label)(A) applies a partition refinement algorithm to minimize the deterministic finite automaton A. The time complexity of this operation is O(n + m.log m), where n is the number of states of the automaton A and m is the number of its transitions. This bound is independent of the size of the alphabet of the transition labels.

Parameters

module Label : sig ... end
module A : sig ... end

Signature

A description of the minimized automaton A'.

A state of the original automaton A is retained only if it is accessible and co-accessible, that is, only if this state lies on a path from some initial state to some final state.

The states that are retained are then grouped into equivalence classes; these equivalence classes form the states of the minimal automaton A'.

The equivalence classes are made as coarse as possible (that is, as large as possible), while obeying the following constraints:

  • The equivalence classes must respect the group of the final states, A.finals. That is, if two states are deemed equivalent, then they must be both final or both non-final.
  • Every group supplied by the user via A.groups must similarly be respected.
  • For every label l, the equivalence classes must be compatible with the transitions that carry the label l. That is, if two states s1 and s2 are deemed equivalent, and if the state s1 has a transition labeled l towards some state s'1, then the state s2 must have a transition labeled l towards some state s'2 such that s'1 and s'2 are also deemed equivalent.
include DFA with type label = Label.t
Sourcetype states

The type states is a type-level representation of the number of states of the automaton. Thus, a state number has type states index. See Indexing for more information about type-level indices.

states is the number of states of the automaton.

A state number is an integer in the range [0, cardinal states).

Sourcetype transitions

The type transitions is a type-level representation of the number of transitions of the automaton. Thus, a transition number has type transitions index. See Indexing for more information about type-level indices.

transitions is the number of transitions of the automaton.

A transition number is an integer in the range [0, cardinal transitions).

Sourcetype label = Label.t

label is the type of transition labels.

Sourceval label : transition -> label

label t returns the label of the transition t.

Sourceval source : transition -> state

source t returns the source state of the transition t.

Sourceval target : transition -> state

target t returns the target state of the transition t.

Sourceval initials : state Enum.enum

initials is an enumeration of the initial states.

Sourceval finals : state Enum.enum

finals is an enumeration of the initial states.

Sourceval transport_state : A.state -> state option

The function transport_state maps a state of the original automaton A to the corresponding state of the minimal automaton A'. It is a partial function: transport_state s is Some _ if and only if the state s lies on a path from some initial state to some final state.

Sourceval transport_transition : A.transition -> transition option

The function transport_transition maps a transition of the original automaton A to the corresponding transition of the minimal automaton A'. It is a partial function: transport_transition t is Some _ if and only if the transition t lies on a path from some initial state to some final state.

Sourceval backport_state_one : state -> A.state

The function backport_state_one maps a state s' of the minimal automaton A' to a state s of the original automaton A such that transport_state s = Some s' holds. There may exist several states s such that this equation holds. A representative state in each equivalence class is chosen, and backport_state_one always returns a representative state.

Sourceval backport_state_all : state -> A.state Enum.enum

The function backport_state_all maps a state s' of the minimal automaton A' to an enumeration of all states s of the original automaton A such that transport_state s = Some s' holds. There exists at least one such state: this enumeration is never empty.

Sourceval backport_transition : transition -> A.transition

The function backport_transition maps a transition t' of the minimal automaton A' to a transition t of the original automaton A such that transport_transition t = Some t' holds. There may exist several transitions t such that this equation holds; backport_transition returns the transition whose source state is a representative state.