Predicate Logic and Tree Automata with Tests
Ralf Treinen
- 25 Mar 2000
- pp 329-343
TL;DR: There is no generalization of tree automata with tests that has a decidable emptiness problem and that is equivalent to the full class of formulae in some extension of WS2S, at least not when the authors are asking for an conservative extension of the classical correspondence.
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Abstract: We investigate the question whether the well-known correspondence between tree automata and the weak second order logic of two successor functions (WS2S) can be extended to tree automata with tests. Our first insight is that there is no generalization of tree automata with tests that has a decidable emptiness problem and that is equivalent to the full class of formulae in some extension of WS2S, at least not when we are asking for an conservative extension of the classical correspondence between WS2S and tree automata to tree automata with tests.
As a consequence we can extend the correspondence between tree automata and WS2S to automata with tests only when we admit a restriction of the class of formulae. We present a logic, called WS2Sy, and a restriction of the class of formula, called uniform, that is equivalent to tree automata with tests.
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Citations
The first-order theory of subtyping constraints
Zhendong Su,Alex Aiken,Joachim Niehren,Tim Priesnitz,Ralf Treinen +4 more
- 01 Jan 2002
TL;DR: It is shown that in the case where all constructors are either unary or nullary, the first-order theory is decidable for both structural and non-structural subtyping, and the decidability results are shown by reduction to a decision problem on tree automata.
Decidable Classes of Tree Automata Mixing Local and Global Constraints Modulo Flat Theories
TL;DR: The decidability of the emptiness problem for TABG is proved and a fragment of the monadic second order logic on trees extended with predicates for equality and disequality between subtrees, and cardinality is proved.
Decidable classes of tree automata mixing local and global constraints modulo flat theories
TL;DR: The decidability of a fragment of the monadic second order logic on trees extended with predicates for equality and disequality between subtrees, and cardinality is proved as a consequence of TABG's results.
24
Thèse de doctorat de l'École Normale Supérieure de Cachan
Monsieur Guillaume Scerri
- 01 Jan 2015
TL;DR: A family of structured sparsity-inducing norms whose properties are closely studied are introduced, and what type of structural prior knowledge they correspond to are shown, and the statistical conditions under which these norms are capable of consistently performing structured variable selection are presented.
Non-structural subtype entailment in automata theory
Joachim Niehren,Tim Priesnitz +1 more
- 01 Nov 2003
TL;DR: Automata theoretic methods are applied to characterize the problem equivalently by using regular expressions and word equations to induces new results on non-structural subtype entailment, constitutes a promising starting point for further investigations on decidability.
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A variant of a recursively unsolvable problem
TL;DR: In this article, the correspondence decision problem is defined as the problem of determining for an arbitrary finite set (gu g{), (g2, g2), • • •, (gM, gi) of pairs of corresponding non-null strings on a, b whether there is a solution in w, iu ii, • •• •, in of equation