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<?xml version="1.0" encoding="ascii"?>
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<a href="pyxb-module.html">Package pyxb</a> ::
<a href="pyxb.utils-module.html">Package utils</a> ::
Module fac
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<!-- ==================== MODULE DESCRIPTION ==================== -->
<h1 class="epydoc">Module fac</h1><p class="nomargin-top"><span class="codelink"><a href="pyxb.utils.fac-pysrc.html">source code</a></span></p>
<p>This module provides Finite Automata with Counters.</p>
<p>FACs are type of state machine where a transition may include a
constraint and a modification to a set of counters. They are used to
implement regular expressions with numerical constraints, as are found in
POSIX regexp, Perl, and XML schema.</p>
<p>The implementation here derives from <a
href="https://bora.uib.no/bitstream/1956/3628/3/Hovland_LNCS%205684.pdf"
target="_top">Regular Expressions with Numerical Constraints and Automata
with Counters</a>, Dag Hovland, Lecture Notes in Computer Science, 2009,
Volume 5684, Theoretical Aspects of Computing - ICTAC 2009, Pages
231-245. In what follows, this reference will be denoted
<b>HOV09</b>.</p>
<p>A regular expression is directly translated into a term tree, where
nodes are operators such as sequence, choice, and counter restrictions,
and the leaf nodes denote symbols in the language of the regular
expression.</p>
<p>In the case of XML content models, the symbols include <a
href="pyxb.xmlschema.structures.ElementDeclaration-class.html"
class="link">element declarations</a> and <a
href="pyxb.xmlschema.structures.Wildcard-class.html"
class="link">wildcard elements</a>. A numerical constraint node
corresponds to an <a href="pyxb.xmlschema.structures.Particle-class.html"
class="link">XML particle</a>, and choice and sequence nodes derive from
<a href="pyxb.xmlschema.structures.ModelGroup-class.html"
class="link">model groups</a> of types <b>choice</b> and <b>sequence</b>.
As suggested in <a href="http://www.ii.uib.no/~dagh/presLATA2012.pdf"
target="_top">The Membership Problem for Regular Expressions with
Unordered Concatenation and Numerical Constraints</a> the <b>all</b>
content model can be translated into state machine using choice and
sequence at the cost of a quadratic size explosion. Since some XML
content models might have a hundred terms in an unordered catenation,
this is not acceptable, and the implementation here optimizes this
construct by creating a leaf node in the automaton which in turn contains
sub-automata for each term, and permits an exit transition only when all
the terms that are required have been completed.</p>
<hr />
<div class="fields"> <p><strong>Note:</strong>
In XSD 1.1 the restriction that terms in an <b>all</b> model group
occur at most once has been removed. Since the current
implementation removes a completed term from the set of available
terms, this will not work: instead the subconfiguration with its
counter values must be retained between matches.
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<a href="pyxb.utils.fac.FACError-class.html" class="summary-name">FACError</a>
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<a href="pyxb.utils.fac.InvalidTermTreeError-class.html" class="summary-name">InvalidTermTreeError</a><br />
Exception raised when a FAC term tree is not a tree.
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<a href="pyxb.utils.fac.UpdateApplicationError-class.html" class="summary-name">UpdateApplicationError</a><br />
Exception raised when an unsatisfied update instruction is
executed.
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<a href="pyxb.utils.fac.AutomatonStepError-class.html" class="summary-name">AutomatonStepError</a><br />
Symbol rejected by <a
href="pyxb.utils.fac.Configuration_ABC-class.html#step"
class="link">Configuration_ABC.step</a>.
</td>
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<td class="summary" colspan="2">
<a href="pyxb.utils.fac.UnrecognizedSymbolError-class.html" class="summary-name">UnrecognizedSymbolError</a><br />
<a href="pyxb.utils.fac.Configuration-class.html#step"
class="link">Configuration.step</a> failed to find a valid
transition.
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<a href="pyxb.utils.fac.NondeterministicSymbolError-class.html" class="summary-name">NondeterministicSymbolError</a><br />
<a href="pyxb.utils.fac.Configuration-class.html#step"
class="link">Configuration.step</a> found multiple transitions.
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<td class="summary" colspan="2">
<a href="pyxb.utils.fac.SymbolMatch_mixin-class.html" class="summary-name">SymbolMatch_mixin</a><br />
Mix-in used by symbols to provide a custom match implementation.
</td>
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<td class="summary" colspan="2">
<a href="pyxb.utils.fac.State-class.html" class="summary-name">State</a><br />
A thin wrapper around an object reference.
</td>
</tr>
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<a href="pyxb.utils.fac.CounterCondition-class.html" class="summary-name">CounterCondition</a><br />
A counter condition is a range limit on valid counter values.
</td>
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<a href="pyxb.utils.fac.UpdateInstruction-class.html" class="summary-name">UpdateInstruction</a><br />
An update instruction pairs a counter with a mutation of that
counter.
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<a href="pyxb.utils.fac.Transition-class.html" class="summary-name">Transition</a><br />
Representation of a FAC state transition.
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<a href="pyxb.utils.fac.Configuration_ABC-class.html" class="summary-name">Configuration_ABC</a><br />
Base class for something that represents an <a
href="pyxb.utils.fac.Automaton-class.html"
class="link">Automaton</a> in execution.
</td>
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<a href="pyxb.utils.fac.Configuration-class.html" class="summary-name">Configuration</a><br />
The state of an <a href="pyxb.utils.fac.Automaton-class.html"
class="link">Automaton</a> in execution.
</td>
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<a href="pyxb.utils.fac.MultiConfiguration-class.html" class="summary-name">MultiConfiguration</a><br />
Support parallel execution of state machine.
</td>
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<td class="summary" colspan="2">
<a href="pyxb.utils.fac.Automaton-class.html" class="summary-name">Automaton</a><br />
Representation of a Finite Automaton with Counters.
</td>
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<a href="pyxb.utils.fac.Node-class.html" class="summary-name">Node</a><br />
Abstract class for any node in the term tree.
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<a href="pyxb.utils.fac.MultiTermNode-class.html" class="summary-name">MultiTermNode</a><br />
Intermediary for nodes that have multiple child nodes.
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<a href="pyxb.utils.fac.LeafNode-class.html" class="summary-name">LeafNode</a><br />
Intermediary for nodes that have no child nodes.
</td>
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<a href="pyxb.utils.fac.NumericalConstraint-class.html" class="summary-name">NumericalConstraint</a><br />
A term with a numeric range constraint.
</td>
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<a href="pyxb.utils.fac.Choice-class.html" class="summary-name">Choice</a><br />
A term that may be any one of a set of terms.
</td>
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<a href="pyxb.utils.fac.Sequence-class.html" class="summary-name">Sequence</a><br />
A term that is an ordered sequence of terms.
</td>
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<a href="pyxb.utils.fac.All-class.html" class="summary-name">All</a><br />
A term that is an unordered sequence of terms.
</td>
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<a href="pyxb.utils.fac.Symbol-class.html" class="summary-name">Symbol</a><br />
A leaf term that is a symbol.
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<a name="__package__"></a><span class="summary-name">__package__</span> = <code title="'pyxb.utils'"><code class="variable-quote">'</code><code class="variable-string">pyxb.utils</code><code class="variable-quote">'</code></code>
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