The equational theory of pomsets
Theoretical Computer Science
The monadic second-order logic of graphs. I. recognizable sets of finite graphs
Information and Computation
MFCS '89 Selected papers of the symposium on Mathematical foundations of computer science
Monadic second-order definable graph transductions: a survey
Theoretical Computer Science - Selected papers of the 17th Colloquium on Trees in Algebra and Programming (CAAP '92) and of the European Symposium on Programming (ESOP), Rennes, France, Feb. 1992
Modulo-counting quantifiers over finite trees
Theoretical Computer Science - Selected papers of the 17th Colloquium on Trees in Algebra and Programming (CAAP '92) and of the European Symposium on Programming (ESOP), Rennes, France, Feb. 1992
Languages, automata, and logic
Handbook of formal languages, vol. 3
Series-parallel languages and the bounded-width property
Theoretical Computer Science
Rationality in algebras with a series operation
Information and Computation
Infinite Series-Parallel Posets: Logic and Languages
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Recognizability Equals Definability for Partial k-Paths
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
A Model Theoretic Proof of Büchi-Type Theorems and First-Order Logic for N-Free Pomsets
STACS '01 Proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science
Regular Tree Languages Without Unary Symbols are Star-Free
FCT '93 Proceedings of the 9th International Symposium on Fundamentals of Computation Theory
Recognizability Equals Monadic Second-Order Definability for Sets of Graphs of Bounded Tree-Width
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
Towards a language theory for infinite N-free pomsets
Theoretical Computer Science
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It is shown that any recognizable set of finite N-free pomsets is axiomatizable in counting monadic second order logic. Differently from similar results by Courcelle, Kabanets, and Lapoire, we do not use MSO-transductions (i.e., one-dimensional interpretations), but two-dimensional interpretations of a generating tree in an N-free pomset. Then we have to deal with the new problem that set-quantifications over the generating tree are translated into quantifications over binary relations in the N-free pomset. This is solved by an adaptation of a result by Potthoff & Thomas on monadic antichain logic.