On the effect of the IO-substitution on the Parikh image of semilinear AFLs
Back in the 80s, the class of mildly context-sensitive formalisms was introduced so as to capture the syntax of natural languages. While the languages generated by such formalisms are constrained by the constant-growth property, the most well-known and used mildly-context sensitive formalisms, like...
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| creator | Bourreau, Pierre |
| description | Back in the 80s, the class of mildly context-sensitive formalisms was
introduced so as to capture the syntax of natural languages. While the
languages generated by such formalisms are constrained by the constant-growth
property, the most well-known and used mildly-context sensitive formalisms,
like tree-adjoining grammars or multiple context-free grammars, generate
languages which verify the stronger property of being semilinear. In (Bourreau
et al., 2012), the operation of IO-ubstitution was created so as to exhibit
mildly context-sensitive classes of languages which are not semilinear,
although they verify the constant-growth property. In the present article, we
extend the notion of semilinearity, and characterise the Parikh image of the
IO-MCFLs (i.e. languages which belong to the closure of MCFLs under
IO-subsitution) as universally-linear. Based on this result and on the work of
Fischer on macro-grammars, we then show IO-MCFLs are not closed under inverse
homomorphism, which proves that the family of IO-MCFLs is not an abstract
family of languages. |
| doi_str_mv | 10.48550/arxiv.1311.0632 |
| format | Article |
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introduced so as to capture the syntax of natural languages. While the
languages generated by such formalisms are constrained by the constant-growth
property, the most well-known and used mildly-context sensitive formalisms,
like tree-adjoining grammars or multiple context-free grammars, generate
languages which verify the stronger property of being semilinear. In (Bourreau
et al., 2012), the operation of IO-ubstitution was created so as to exhibit
mildly context-sensitive classes of languages which are not semilinear,
although they verify the constant-growth property. In the present article, we
extend the notion of semilinearity, and characterise the Parikh image of the
IO-MCFLs (i.e. languages which belong to the closure of MCFLs under
IO-subsitution) as universally-linear. Based on this result and on the work of
Fischer on macro-grammars, we then show IO-MCFLs are not closed under inverse
homomorphism, which proves that the family of IO-MCFLs is not an abstract
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introduced so as to capture the syntax of natural languages. While the
languages generated by such formalisms are constrained by the constant-growth
property, the most well-known and used mildly-context sensitive formalisms,
like tree-adjoining grammars or multiple context-free grammars, generate
languages which verify the stronger property of being semilinear. In (Bourreau
et al., 2012), the operation of IO-ubstitution was created so as to exhibit
mildly context-sensitive classes of languages which are not semilinear,
although they verify the constant-growth property. In the present article, we
extend the notion of semilinearity, and characterise the Parikh image of the
IO-MCFLs (i.e. languages which belong to the closure of MCFLs under
IO-subsitution) as universally-linear. Based on this result and on the work of
Fischer on macro-grammars, we then show IO-MCFLs are not closed under inverse
homomorphism, which proves that the family of IO-MCFLs is not an abstract
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introduced so as to capture the syntax of natural languages. While the
languages generated by such formalisms are constrained by the constant-growth
property, the most well-known and used mildly-context sensitive formalisms,
like tree-adjoining grammars or multiple context-free grammars, generate
languages which verify the stronger property of being semilinear. In (Bourreau
et al., 2012), the operation of IO-ubstitution was created so as to exhibit
mildly context-sensitive classes of languages which are not semilinear,
although they verify the constant-growth property. In the present article, we
extend the notion of semilinearity, and characterise the Parikh image of the
IO-MCFLs (i.e. languages which belong to the closure of MCFLs under
IO-subsitution) as universally-linear. Based on this result and on the work of
Fischer on macro-grammars, we then show IO-MCFLs are not closed under inverse
homomorphism, which proves that the family of IO-MCFLs is not an abstract
family of languages.</abstract><doi>10.48550/arxiv.1311.0632</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Computer Science - Formal Languages and Automata Theory |
| title | On the effect of the IO-substitution on the Parikh image of semilinear AFLs |
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