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One was a trivial definition for a finite language; it simply listed the finitely many true sentences.
This paper describes an evolutionary approach to the problem of inferring stochastic context-free grammars from finite language samples.
The Maximum Asymmetric Travelling Salesman Problem (Max-ATSP), which asks for a Hamiltonian path of maximum weight covering a digraph, and the Maximum Compression(Max-Comp), which, for a finite language P≔{s1,…,sp}, asks for w, a superstring of P minimising ∑si∈S|si|−|w|, are both difficult to approximate (Max-SNP hard).
(As Quine (1970) points out, however, a finite language will always contain a predicate satisfying Ref and LL in any structure; cf. Hodges 1983).
Leaping too soon to the conclusion that the target language is infinite will be disastrous, because there will be no way to retrench: no presented examples from a finite language Lk will ever conflict with the hypothesis that the target is some infinite superset of Lk.
Zellig Harris, an archetypal Externalist, is explicit that the reason for not regarding the set of utterances as finite concerns the elegance of the resulting grammar: "If we were to insist on a finite language, we would have to include in our grammar several highly arbitrary and numerical conditions" (Harris 1957: 208).
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In this paper, we propose a self-reconfiguring control architecture, state our reconfiguration problem in terms of finite languages and address the synthesis of discrete event dynamic reconfiguration blocks.
This claim (for which Chomsky had little basis: see Pullum 1983) would immediately guarantee that not all finite languages are humanly learnable (there are infinitely many finite languages, so for most of them there would be no permissible grammar).
Conversely, we prove in this paper that, on a finite prepositional language, any preferential inference relation defined by such a model is induced by a Poole system without constraints.
Languages L are called finite-quantifier languages, the rest infinite-quantifier languages.
Perhaps the most salient and famous is the issue of whether English is a finite-state language.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com