Finite automata and unary languages
Theoretical Computer Science
A note on the number of monadic quantifiers in monadic S11
Information Processing Letters
On a monadic NP vs monadic co-NP
Information and Computation
Monadic second-order logic over rectangular pictures and recognizability by tiling systems
Information and Computation
Handbook of formal languages, vol. 3
The closure of Monadic NP (extended abstract)
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Automata, Languages, and Machines
Automata, Languages, and Machines
Dot-depth, monadic quantifier alternation, and first-order closure over grids and pictures
Theoretical Computer Science
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
One Quantifier Will Do in Existential Monadic Second-Order Logic over Pictures
MFCS '98 Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science
The Monadic Quantifier Alternation Hierarchy over Grids and Pictures
CSL '97 Selected Papers from the11th International Workshop on Computer Science Logic
The Monadic Quantifier Alternation Hierarchy over Graphs is Infinite
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
On the expressive power of monadic least fixed point logic
Theoretical Computer Science - Automata, languages and programming: Logic and semantics (ICALP-B 2004)
Message-passing automata are expressively equivalent to EMSO logic
Theoretical Computer Science - Concurrency theory (CONCUR 2004)
Arity and alternation: a proper hierarchy in higher order logics
Annals of Mathematics and Artificial Intelligence
Note: Existential MSO over two successors is strictly weaker than over linear orders
Theoretical Computer Science
Uniform satisfiability problem for local temporal logics over Mazurkiewicz traces
Information and Computation
Extensions of MSO and the monadic counting hierarchy
Information and Computation
Comparing necessary conditions for recognizability of two-dimensional languages
CAI'11 Proceedings of the 4th international conference on Algebraic informatics
Nested pebbles and transitive closure
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Arity and alternation: a proper hierarchy in higher order logics
FoIKS'06 Proceedings of the 4th international conference on Foundations of Information and Knowledge Systems
On the expressiveness of asynchronous cellular automata
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
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The monadic second-order quantifier alternation hierarchy over the class of finite graphs is shown to be strict. The proof is based on automata theoretic ideas and starts from a restricted class of graph-like structures, namely finite two-dimensional grids. Considering grids where the width is a function of the height, we prove that the difference between the levels k + 1 and k of the monadic hierarchy is witnessed by a set of grids where this function is (k + 1)-fold exponential. We then transfer the hierarchy result to the class of directed (or undirected) graphs, using an encoding technique called strong reduction. It is notable that one can obtain sets of graphs which occur arbitrarily high in the monadic hierarchy but are already definable in the first-order closure of existential monadic second-order logic. We also verify that these graph properties even belong to the complexity class NLOG. which indicates a profound difference between the monadic hierarchy and the polynomial hierarchy.