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• W1581235941 abstract "Recently, we have shown that satisfiability for $mathsf{ECTL}^*$ with constraints over $mathbb{Z}$ is decidable using a new technique. This approach reduces the satisfiability problem of $mathsf{ECTL}^*$ with constraints over some structure A (or class of structures) to the problem whether A has a certain model theoretic property that we called EHD (for existence of homomorphisms is decidable). Here we apply this approach to concrete domains that are tree-like and obtain several results. We show that satisfiability of $mathsf{ECTL}^*$ with constraints is decidable over (i) semi-linear orders (i.e., tree-like structures where branches form arbitrary linear orders), (ii) ordinal trees (semi-linear orders where the branches form ordinals), and (iii) infinitely branching trees of height h for each fixed $hin mathbb{N}$. We prove that all these classes of structures have the property EHD. In contrast, we introduce Ehrenfeucht-Fraisse-games for $mathsf{WMSO}+mathsf{B}$ (weak $mathsf{MSO}$ with the bounding quantifier) and use them to show that the infinite (order) tree does not have property EHD. As a consequence, a different approach has to be taken in order to settle the question whether satisfiability of $mathsf{ECTL}^*$ (or even $mathsf{LTL}$) with constraints over the infinite (order) tree is decidable." @default.
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• W1581235941 date "2014-12-09" @default.
• W1581235941 modified "2023-09-27" @default.
• W1581235941 title "Satisfiability of ECTL* with tree constraints" @default.
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