Module: Regular Expressions (`reex`)¶

Regular expressions manipulation

Regular expression classes and manipulation

Classes¶

RegularExpression¶

class RegularExpression[source]¶: Abstract base class for all regular expression objects

RegExp¶

class RegExp(sigma=None)[source]¶

Base class for regular expressions.

Variables: Sigma – alphabet set of strings

abstract static alphabeticLength()[source]¶

Number of occurrences of alphabet symbols in the regular expression.

Return type: integer

Attention

Doesn’t include the empty word.

compare(r, cmp_method='compareMinimalDFA', nfa_method='nfaPD')[source]¶: Compare with another regular expression for equivalence. :param r: :param cmp_method: :param nfa_method:

compareMinimalDFA(r, nfa_method='nfaPosition')[source]¶: Compare with another regular expression for equivalence through minimal DFAs. :param r: :param nfa_method:

dfaAuPoint()[source]¶

DFA “au-point” acconding to Nipkow

Returns: “au-point” DFA
Return type: fa.DFA

See also

Andrea Asperti, Claudio Sacerdoti Coen and Enrico Tassi, Regular Expressions, au point. arXiv 2010

See also

Tobias Nipkow and Dmitriy Traytel, Unified Decision Procedures for

Regular Expression Equivalence

dfaBrzozowski(memo=None)[source]¶

Word derivatives automaton of the regular expression

Returns: word derivatives automaton
Return type: DFA

See also

1. Brzozowski, Derivatives of Regular Expressions. J. ACM 11(4): 481-494 (1964)

dfaYMG()[source]¶

DFA Yamada-McNaugthon-Gluskov acconding to Nipkow

Returns: Y-M-G DFA
Return type: DFA

See also

Tobias Nipkow and Dmitriy Traytel, Unified Decision Procedures for

Regular Expression Equivalence

static emptysetP()[source]¶

Whether the regular expression is the empty set.

Return type: Boolean

abstract static epsilonLength()[source]¶

Number of occurrences of the empty word in the regular expression.

Return type: integer

static epsilonP()[source]¶

Whether the regular expression is the empty word.

Return type: Boolean

equivP(other, strict=True)[source]¶

Test RE equivalence with extended Hopcroft-Karp method

Parameters

other (RegExp) – RE
strict (bool) – if True checks for same alphabets

Return type

bool

equivalentP(other)[source]¶

Tests equivalence

Parameters: other –
Return type: bool

evalWordP(word)[source]¶

Verifies if a word is a member of the language represented by the regular expression.

Parameters: word (str) – the word
Return type: bool

static ewp()[source]¶

Whether the empty word property holds for this regular expression’s language.

Return type: Boolean

abstract first()[source]¶

Return type: set

abstract last()[source]¶

Return type: set

abstract linearForm()[source]¶

Return type: dic

abstract mark()[source]¶: Make all atoms maked (tag False) :rtype: RegExp

marked()[source]¶

Regular expression in which every alphabetic symbol is marked with its Position.

The kind of regular expression returned is known, depending on the literary source, as marked, linear or restricted regular expression.

Returns: linear regular expression
Return type: RegExp

See also

r. McNaughton and H. Yamada, Regular Expressions and State Graphs for Automata, IEEE Transactions on Electronic Computers, V.9 pp:39-47, 1960

..attention: mark and unmark do not preserve the alphabet, neither set the new alphabet

nfaFollow()[source]¶

NFA that accepts the regular expression’s language, whose structure, equiand construction.

Return type: NFA

See also

Ilie & Yu (Follow Automata, 03)

nfaFollowEpsilon(trim=True)[source]¶

Epsilon-NFA constructed with Ilie and Yu’s method () that accepts the regular expression’s language.

Parameters: trim –
Returns: NFA possibly with CEpsilon transitions
Return type: NFAe

Note

The regular expression must be reduced

See also

Ilie & Yu, Follow automta, Inf. Comp. ,v. 186 (1),140-162,2003

nfaGlushkov()[source]¶

Position or Glushkov automaton of the regular expression. Recursive method.

Returns: NFA

nfaNaiveFollow()[source]¶

NFA that accepts the regular expression’s language, and is equal in structure to the follow automaton.

Return type: NFA

Note

Included for testing purposes.

See also

Ilie & Yu (Follow Automata, 2003)

nfaPD(pdmethod='nfaPDDAG')[source]¶: Computes the partial derivative automaton : param pdmethod str: an implementation of the PD automaton. Default value : nfaPDDAG :return: a PD nfa :rtype: NFA

nfaPDDAG()[source]¶

” :return: a PD nfa build using a DAG :rtype: NFA

..seealso:: s.Konstantinidis, A. Machiavelo, N. Moreira, and r. Reis.: Partial derivative automaton by compressing regular expressions. DCFS 2021, volume 13037 of LNCS, pages 100–112. Springer, 2022

nfaPDNaive()[source]¶

NFA that accepts the regular expression’s language,: and which is constructed from the expression’s partial derivatives.
Returns: NFA: partial derivatives [or equation] automaton

See also

V. M. Antimirov, Partial Derivatives of Regular Expressions and Finite Automaton Constructions .Theor. Comput. Sci.155(2): 291-319 (1996)

nfaPDO()[source]¶

NFA that accepts the regular expression’s language, and which is constructed from the expression’s partial: derivatives.

Note

optimized version

Returns: partial derivatives [or equation] automaton
Return type: NFA

nfaPSNF()[source]¶

Position or Glushkov automaton of the regular expression constructed from the expression’s star normal form.

Returns: Position automaton
Return type: NFA

nfaPosition(lstar=True)[source]¶

Position automaton of the regular expression.

Parameters: lstar (boolean) – if not None followlists are computed as disjunct
Returns: Position NFA
Return type: NFA

nfaPre()[source]¶: Prefix NFA of a regular expression States are of the form (RegExp,sym) :return: prefix automaton :rtype: NFA

See also

Maia et al, Prefix and Right-partial derivative automata, 11th CIE 2015, 258-267 LNCS 9136, 2015

nfaPreSlow()[source]¶: Prefix NFA of a regular expression :return: prefix automaton :rtype: NFA .. seealso:: Maia et al, Prefix and Right-partial derivative automata, 11th CIE 2015, 258-267 LNCS 9136, 2015 ..note:: not working with current tailForm

notEmptyW()[source]¶

Witness of non emptyness

Returns: word or None

abstract rpn()[source]¶: RPN representation :rtype: str :return: printable RPN representation

abstract static setOfSymbols()[source]¶

Return type: set

setSigma(symbolset=None, strict=False)[source]¶

Set the alphabet for a regular expression and all its nodes

Parameters

symbolset (list or set of str) – accepted symbols. If None, alphabet is unset.
strict (bool) – if True checks if setOfSymbols is included in symbolSet

..attention: Normally this attribute is not defined in a RegExp()

abstract static starHeight()[source]¶

Maximum level of nested regular expressions with a star operation applied.

For instance, starHeight(((a*b)*+b*)*) is 3.

Return type: integer

abstract tailForm()[source]¶

Return type: dict

toDFA()[source]¶: DFA that accepts the regular expression’s language

toNFA(nfa_method='nfaPDNaive')[source]¶: NFA that accepts the regular expression’s language. :param nfa_method:

abstract static treeLength()[source]¶

Number of nodes of the regular expression’s syntactical tree.

Return type: integer

unionSigma(other)[source]¶

Returns the union of two alphabets

Return type: set

wordDerivative(word)[source]¶

Derivative of the regular expression in relation to the given word,: which is represented by a list of symbols.

Parameters: word – list of arbitrary symbols.
Return type: regular expression

See also

1. Brzozowski, Derivatives of Regular Expressions. J. ACM 11(4): 481-494 (1964)

SpecialConstant¶

class SpecialConstant(sigma=None)[source]¶

Base class for Epsilon and EmptySet

Parameters: sigma – alphabet

static alphabeticLength()[source]¶

Returns

derivative(sigma)[source]¶

Parameters: sigma –
Returns

distDerivative(sigma)[source]¶

Parameters: sigma – an arbitrary symbol.
Return type: regular expression

static epsilonLength()[source]¶

Number of occurrences of the empty word in the regular expression.

Return type: integer

static first(parent_first=None)[source]¶

Parameters: parent_first –
Returns

followLists(lists=None)[source]¶

Parameters: lists –
Returns

followListsD(lists=None)[source]¶

Parameters: lists –
Returns

static followListsStar(lists=None)[source]¶

Parameters: lists –
Returns

last(parent_last=None)[source]¶

Parameters: parent_last –
Returns

linearForm()[source]¶

Returns

mark()[source]¶: Make all atoms maked (tag False) :rtype: RegExp

partialDerivativesC(sigma)[source]¶

Parameters: sigma –
Returns

reversal()[source]¶

Reversal of RegExp

Return type: reex.RegExp

abstract rpn()[source]¶: RPN representation :rtype: str :return: printable RPN representation

static setOfSymbols()[source]¶

Returns

static starHeight()[source]¶

Maximum level of nested regular expressions with a star operation applied.

For instance, starHeight(((a*b)*+b*)*) is 3.

Return type: integer

support(side=True)[source]¶

Returns

supportlast(side=True)[source]¶

Returns

tailForm()[source]¶

Returns

static treeLength()[source]¶

Number of nodes of the regular expression’s syntactical tree.

Return type: integer

unmark()[source]¶: Conversion back to unmarked atoms :rtype: SpecialConstant

unmarked()[source]¶

The unmarked form of the regular expression. Each leaf in its syntactical tree becomes a RegExp(), the CEpsilon() or the CEmptySet().

Return type: (general) regular expression

wordDerivative(word)[source]¶

Parameters: word –
Returns

CEpsilon¶

class CEpsilon(sigma=None)[source]¶

Class that represents the empty word.

Parameters: sigma – alphabet

static epsilonLength()[source]¶

Number of occurrences of the empty word in the regular expression.

Return type: integer

static epsilonP()[source]¶

Return type: bool

static ewp()[source]¶

Return type: bool

static measure(from_parent=None)[source]¶

Parameters: from_parent –
Returns: measures

nfaThompson()[source]¶

Return type: NFA

partialDerivatives(_)[source]¶

Returns

partialDerivativesC(_)[source]¶

Returns

rpn()[source]¶

Returns: str

snf(_hollowdot=False)[source]¶

Parameters: _hollowdot –
Returns

CEmptySet¶

class CEmptySet(sigma=None)[source]¶

Class that represents the empty set.

Parameters: sigma – alphabet

static emptysetP()[source]¶

Returns

static epsilonLength()[source]¶

Returns

static epsilonP()[source]¶

Returns

static ewp()[source]¶

Returns

static measure(from_parent=None)[source]¶

Parameters: from_parent –
Returns

nfaPD(pdmethod='nfaPDNaive')[source]¶: Computes the partial derivative automaton

partialDerivativesC(_)[source]¶

Returns

rpn()[source]¶

Returns

SigmaP¶

SigmaP¶: alias of @sigmaP

SigmaS¶

SigmaS¶: alias of @sigmaS

Connective¶

class Connective(arg1, arg2, sigma=None)[source]¶

Base class for (binary) operations: concatenation, disjunction, etc

alphabeticLength()[source]¶

Number of occurrences of alphabet symbols in the regular expression.

Return type: integer

Attention

Doesn’t include the empty word.

epsilonLength()[source]¶

Number of occurrences of the empty word in the regular expression.

Return type: integer

first(parent_first=None)[source]¶

Return type: set

last(parent_last=None)[source]¶

Return type: set

abstract linearForm()[source]¶

Return type: dic

abstract mark()[source]¶: Make all atoms maked (tag False) :rtype: RegExp

abstract rpn()[source]¶: RPN representation :rtype: str :return: printable RPN representation

setOfSymbols()[source]¶

Return type: set

starHeight()[source]¶

Maximum level of nested regular expressions with a star operation applied.

For instance, starHeight(((a*b)*+b*)*) is 3.

Return type: integer

treeLength()[source]¶

Number of nodes of the regular expression’s syntactical tree.

Return type: integer

Star¶

Concat¶

Disj¶

Power¶

class Power(arg, n=1, sigma=None)[source]¶

Class for Power operation on regular expressions.

alphabeticLength()[source]¶

Number of occurrences of alphabet symbols in the regular expression.

Return type: integer

Attention

Doesn’t include the empty word.

epsilonLength()[source]¶

Number of occurrences of the empty word in the regular expression.

Return type: integer

first()[source]¶

Return type: set

last()[source]¶

Return type: set

linearForm()[source]¶

Return type: dic

mark()[source]¶: Make all atoms maked (tag False) :rtype: RegExp

reversal()[source]¶

Reversal of RegExp

Return type: reex.RegExp

rpn()[source]¶: RPN representation :rtype: str :return: printable RPN representation

setOfSymbols()[source]¶

Return type: set

starHeight()[source]¶

Maximum level of nested regular expressions with a star operation applied.

For instance, starHeight(((a*b)*+b*)*) is 3.

Return type: integer

tailForm()[source]¶

Return type: dict

treeLength()[source]¶

Number of nodes of the regular expression’s syntactical tree.

Return type: integer

Option¶

Option¶: alias of -

Conj¶

Conj¶: alias of &

Shuffle¶

Shuffle¶: alias of :

Atom¶

Position¶

class Position(val, sigma=None)[source]¶

Class for marked regular expression symbols.

Constructor of a regular expression symbol.

Parameters: val – the actual symbol

setOfSymbols()[source]¶

Set of symbols that occur in a regular expression..

Returns: set of symbols
Return type: set of symbols

unmarked()[source]¶

The unmarked form of the regular expression. Each leaf in its syntactical tree becomes a RegExp(), the CEpsilon() or the CEmptySet().

Return type: (general) regular expression

SConnective¶

class SConnective(arg, sigma=None)[source]¶

Special regular expressions modulo associativity, commutativity, idempotence of disjunction and intersection;

associativity of concatenation; identities sigma^* and sigma^+. Connectives are:

SDisj: disjunction SConj: intersection SConcat: concatenation

For parsing use str2sre

alphabeticLength()[source]¶

Returns

epsilonLength()[source]¶

Returns

first()[source]¶

Return type: set

last()[source]¶

Return type: set

linearForm()[source]¶

Return type: dic

mark()[source]¶: Make all atoms maked (tag False) :rtype: RegExp

nfaPD(pdmethod='nfaPDNaive')[source]¶: Computes the partial derivative automaton

rpn()[source]¶: RPN representation :rtype: str :return: printable RPN representation

setOfSymbols()[source]¶

Returns

starHeight()[source]¶

Maximum level of nested regular expressions with a star operation applied.

For instance, starHeight(((a*b)*+b*)*) is 3.

Return type: integer

syntacticLength()[source]¶

Returns

abstract tailForm()[source]¶

Return type: dict

treeLength()[source]¶

Returns

SConcat¶

class SConcat(arg, sigma=None)[source]¶

Class that represents the concatenation operation.

derivative(sigma)[source]¶

Parameters: sigma –
Returns

ewp()[source]¶

Returns

head()[source]¶

Returns

head_rev()[source]¶

Returns

linearForm()[source]¶

Returns

linearFormC()[source]¶

Returns

partialDerivatives(sigma)[source]¶

Parameters: sigma –
Returns

partialDerivativesC(sigma)[source]¶

Parameters: sigma –
Returns

support(side=True)[source]¶

Returns

tail()[source]¶

Returns

tailForm()[source]¶

Return type: dict

tail_rev()[source]¶

Returns

SStar¶

class SStar(arg, sigma=None)[source]¶

Special regular expressions modulo associativity, commutativity, idempotence of disjunction and intersection;: associativity of concatenation; identities sigma^* and sigma^+.

SStar: Class that represents Kleene star

derivative(sigma)[source]¶

Parameters: sigma –
Returns

linearForm()[source]¶

Returns

nfaPD(pdmethod='nfaPDNaive')[source]¶: Computes the partial derivative automaton

partialDerivatives(sigma)[source]¶

Parameters: sigma –
Returns

partialDerivativesC(sigma)[source]¶

Parameters: sigma –
Returns

support(side=True)[source]¶

Returns

SDisj¶

class SDisj(arg, sigma=None)[source]¶

Class that represents the disjunction operation for special regular expressions.

static cross(ri, s, lists)[source]¶

Return type: list

derivative(sigma)[source]¶

Parameters: sigma –
Returns

ewp()[source]¶

Returns

first()[source]¶

Returns

followLists(lists=None)[source]¶

Parameters: lists –
Returns

followListsStar(lists=None)[source]¶

Parameters: lists –
Returns

last()[source]¶

Returns

linearForm()[source]¶

Returns

linearFormC()[source]¶

Returns

partialDerivatives(sigma)[source]¶

Parameters: sigma –
Returns

partialDerivativesC(sigma)[source]¶

Parameters: sigma –
Returns

support(side=True)[source]¶

Returns

tailForm()[source]¶

Return type: dict

SConj¶

class SConj(arg, sigma=None)[source]¶

Class that represents the conjunction operation.

derivative(sigma)[source]¶

Parameters: sigma –
Returns

ewp()[source]¶

Returns

linearForm()[source]¶

Returns

partialDerivatives(sigma)[source]¶

Parameters: sigma –
Returns

partialDerivativesC(sigma)[source]¶

Parameters: sigma –
Returns

support(side=True)[source]¶

Returns

tailForm()[source]¶

Return type: dict

SNot¶

class SNot(arg, sigma=None)[source]¶

Special regular expressions modulo associativity, commutativity, idempotence of disjunction and intersection;: associativity of concatenation; identities sigma^* and sigma^+. SNot: negation

alphabeticLength()[source]¶

Returns

derivative(sigma)[source]¶: :param sigma :return:

epsilonLength()[source]¶

Returns

ewp()[source]¶

Returns

first()[source]¶

Return type: set

last()[source]¶

Return type: set

linearForm()[source]¶

Returns

linearFormC()[source]¶

Returns

mark()[source]¶: Make all atoms maked (tag False) :rtype: RegExp

nfaPD(pdmethod='nfaPDNaive')[source]¶: Computes the partial derivative automaton

partialDerivatives(sigma)[source]¶

Parameters: sigma –
Returns

partialDerivativesC(sigma)[source]¶

Parameters: sigma –
Returns

rpn()[source]¶: RPN representation :rtype: str :return: printable RPN representation

setOfSymbols()[source]¶

Returns

starHeight()[source]¶

Maximum level of nested regular expressions with a star operation applied.

For instance, starHeight(((a*b)*+b*)*) is 3.

Return type: integer

support(side=True)[source]¶

Returns

syntacticLength()[source]¶

Returns

tailForm()[source]¶

Return type: dict

treeLength()[source]¶

Returns

DAG¶

class DAG(reg)[source]¶

Class to support dags representing regexps

…seealso: P. Flajolet, P. Sipala, J.-M. Steyaert, Analytic variations on the common subexpression problem,: in: Automata, Languages and Programmin, LNCS, vol. 443, Springer, New York, 1990, pp. 220–234.

Variables: reg (reex) – regular expression

catLF(idl, idr, delay=False)[source]¶: both arguments are assumed to be already present in the DAG

static plusLF(diff1, diff2)[source]¶

Union of partial derivatives

Parameters

diff1 (dict) – partial diff of the first argument
diff2 (dict) – partial diff of the second argument

Return type

dict

DNode¶

class DNode(op, arg1=None, arg2=None)[source]¶

MAtom¶

class MAtom(val, mark, sigma=None)[source]¶

Base class for pointed (marked) regular expressions

Used directly to represent atoms (characters). This class is used to obtain Yamada or Asperti automata. There is no evident use for it, outside this module.

Parameters

val – symbol
sigma – alphabet

unmark()[source]¶

Conversion back to RegExp

Return type: reex.RegExp

BuildRegexp¶

class BuildRegexp(context=None)[source]¶: Semantics of the FAdo grammars’ regexps Priorities of operators: disj > conj > shuffle > concat > not > star >= option

BuildRPNRegexp¶

class BuildRPNRegexp(context=None)[source]¶

BuildRPNSRE¶

class BuildRPNSRE(context=None)[source]¶

BuildSRE¶

class BuildSRE(context=None)[source]¶: Parser for sre

Functions¶

str2regexp¶

str2regexp(s, parser=Lark(open('/Users/rvr/Work/FAdo/FAdo/regexp_grammar.lark'), parser='lalr', lexer='contextual', ...), sigma=None, strict=False)[source]¶

Reads a RegExp from string.

Parameters

s (string) – the string representation of the regular expression
parser – a parser generator for regexps
sigma (list or set of symbols) – alphabet of the regular expression
strict (boolean) – if True tests if the symbols of the regular expression are included in sigma

Return type

reex.RegExp

str2sre¶

str2sre(s, parser=Lark(open('/Users/rvr/Work/FAdo/FAdo/regexp_grammar.lark'), parser='lalr', lexer='contextual', ...), sigma=None, strict=False)[source]¶

Reads a sre from string. Arguments as str2regexp.

Return type: reex.sre

rpn2regexp¶

rpn2regexp(s, sigma=None, strict=False)[source]¶

Reads a (simple) RegExp from a RPN representation

r ::=  .RR | +RR | *r | L | @
L ::=  [a-z] | [A-Z]

Parameters

s (str) – RPN representation
strict (bool) – Boolean
sigma (set) – alphabet

Return type

reex.RegExp

Note

This method uses python stack… thus depth limitations apply

to_s¶

to_s(r)[source]¶

Returns a sre from FAdo regexp.

Parameters: r (RegExp) – the FAdo representation regexp for a regular expression.
Return type: RegExp

Module: Regular Expressions (`reex`)¶

Classes¶

RegularExpression¶

RegExp¶

SpecialConstant¶

CEpsilon¶

CEmptySet¶

SigmaP¶

SigmaS¶

Connective¶

Star¶

Concat¶

Disj¶

Power¶

Option¶

Conj¶

Shuffle¶

Atom¶

Position¶

SConnective¶

SConcat¶

SStar¶

SDisj¶

SConj¶

SNot¶

DAG¶

DNode¶

MAtom¶

BuildRegexp¶

BuildRPNRegexp¶

BuildRPNSRE¶

BuildSRE¶

Functions¶

str2regexp¶

str2sre¶

rpn2regexp¶

to_s¶

Table of Contents

This Page

Module: Regular Expressions (reex)¶

Classes¶

RegularExpression¶

RegExp¶

SpecialConstant¶

CEpsilon¶

CEmptySet¶

SigmaP¶

SigmaS¶

Connective¶

Star¶

Concat¶

Disj¶

Power¶

Option¶

Conj¶

Shuffle¶

Atom¶

Position¶

SConnective¶

SConcat¶

SStar¶

SDisj¶

SConj¶

SNot¶

DAG¶

DNode¶

MAtom¶

BuildRegexp¶

BuildRPNRegexp¶

BuildRPNSRE¶

BuildSRE¶

Functions¶

str2regexp¶

str2sre¶

rpn2regexp¶

to_s¶

Module: Regular Expressions (`reex`)¶