Handbook of theoretical computer science (vol. B)
Languages, automata, and logic
Handbook of formal languages, vol. 3
Dynamic Logic
Introduction to Formal Language Theory
Introduction to Formal Language Theory
Ehrenfeucht Games, the Composition Method, and the Monadic Theory of Ordinal Words
Structures in Logic and Computer Science, A Selection of Essays in Honor of Andrzej Ehrenfeucht
Model Checking Synchronized Products of Infinite Transition Systems
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
On compositionality and its limitations
ACM Transactions on Computational Logic (TOCL)
Model theory makes formulas large
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Compositional failure detection in structured transition systems
CIAA'11 Proceedings of the 16th international conference on Implementation and application of automata
LTL-Model-Checking via model composition
RP'12 Proceedings of the 6th international conference on Reachability Problems
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The compositional method, introduced by Feferman and Vaught in 1959, allows to reduce the model-checking problem for a product structure to the model-checking problem for its factors. It applies to first-order logic, and limitations for its use have recently been revealed by Rabinovich (2007). We sharpen the results of Rabinovich by showing that the composition method is applicable to the asynchronous product (and the finitely synchronized product) for an extended modal logic in which the reachability modality is enhanced by a (semi-linear) condition on path lengths. We show that a slight extension leads to the failure of the composition theorem. We add comments on extensions of the result and open questions.