Finite automata and unary languages
Theoretical Computer Science
Monadic second-order logic over rectangular pictures and recognizability by tiling systems
Information and Computation
Handbook of formal languages, vol. 3
Context-sensitive string languages and recognizable picture languages
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The closure of Monadic NP (extended abstract)
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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
On Some Recognizable Picture-Languages
MFCS '98 Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science
Star-Free Picture Expressions are Strictly Weaker Than First-Order Logic
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
On Piecewise Testable, Starfree, and Recognizable Picture Languages
FoSSaCS '98 Proceedings of the First International Conference on Foundations of Software Science and Computation Structure
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
New Results on Alternating and Non-deterministic Two-Dimensional Finite-State Automata
STACS '01 Proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science
The monadic quantifier alternation hierarchy over grids and graphs
Information and Computation - Special issue: LICS'97
Automata logics, and infinite games
Deterministic and unambiguous two-dimensional languages over one-letter alphabet
Theoretical Computer Science
Fundamenta Informaticae - Machines, Computations and Universality, Part II
CAI '09 Proceedings of the 3rd International Conference on Algebraic Informatics
Recognizable vs. regular picture languages
CAI'07 Proceedings of the 2nd international conference on Algebraic informatics
Deterministic two-dimensional languages over one-letter alphabet
CAI'07 Proceedings of the 2nd international conference on Algebraic informatics
Fundamenta Informaticae - Machines, Computations and Universality, Part II
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This paper presents results from two different areas. The first area is monadic second-order logic (MSO) over finite structures, in particular over the so-called grids. These are structures whose elements can be arranged as a matrix and which have two binary relations corresponding to vertical and horizontal successors. For this logic, we study the expressive power of the alternation of existential and universal monadic second-order quantifiers, i.e., set quantifiers. In Matz et al. (Information and Computation, LICS' 97, 1999, to appear) it had been shown that these alternations cannot be limited to a fixed number without loss of expressiveness. In this paper, we strengthen this result in several ways. Firstly, we show that there are MSO formulas that have a very restricted form of k+1 set quantifiers but are not equivalent to a formula with k quantifiers. Secondly, we show that if we fix the number of such alternations, the expressive power of formulas that start with a block of universal quantifiers differs from the power of those that start with an existential one this was previously known only for coloured grids. Thirdly, we investigate how an additional prefix of first-order (i.e., element) quantifiers influences the expressive power of MSO formulas. The second area that this paper is concerned with is two-dimensional formal language theory. We study how the alternation of (first- and monadic second-order) quantifications, on the one hand, relates to the dot-depth measure of two-dimensional (i.e., picture) languages, on the other hand. That measure is the two-dimensional version of the classical notion of dot-depth for (one-dimensional) starfree word languages. We show that the hierarchy induced by this dot-depth cuts through the hierarchy given by monadic second-order quantifications. In particular, beyond each level of the monadic second-order alternation hierarchy, there is a starfree picture language.