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Logic and rational languages of scattered and countable series-parallel posets
Theoretical Computer Science ( IF 0.9 ) Pub Date : 2020-01-20 , DOI: 10.1016/j.tcs.2020.01.015
Amazigh Amrane , Nicolas Bedon

Let A be an alphabet and SP(A) denote the class of all countable N-free partially ordered sets labeled by A, in which chains are scattered linear orderings and antichains are finite. We characterize the rational languages of SP(A) by means of logic. We define an extension of monadic second-order logic by Presburger arithmetic, named P-MSO, such that a language L of SP(A) is rational if and only if L is the language of a sentence of P-MSO, with effective constructions from one formalism to the other. As a corollary, the P-MSO theory of SP(A) is decidable.



中文翻译:

分散且可数的串并行摆态的逻辑和有理语言

A为字母,小号P一种表示由A标记的所有可计数的无N部分偏序集的类别,其中链是分散的线性排序,而反链是有限的。我们刻画了小号P一种通过逻辑。我们通过Presburger算术定义了单子二阶逻辑的扩展,称为P-MSO,使得语言L小号P一种当且仅当L是P-MSO句子的语言,并且具有从一种形式主义到另一种形式主义的有效构造时,它才是合理的。因此,P-MSO理论小号P一种 是可以决定的。

更新日期:2020-01-20
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