Succinct representations of graphs
Information and Control
A note on succinct representations of graphs
Information and Control
Efficient solution to connectivity problems on hierarchically defined graphs
SIAM Journal on Computing
The method of forced enumeration for nondeterministic automata
Acta Informatica
Nondeterministic space is closed under complementation
SIAM Journal on Computing
Hierarchical planarity testing algorithms
Journal of the ACM (JACM)
Expressibility and parallel complexity
SIAM Journal on Computing
The monadic second-order logic of graphs. I. recognizable sets of finite graphs
Information and Computation
Journal of Computer and System Sciences - 3rd Annual Conference on Structure in Complexity Theory, June 14–17, 1988
Graph rewriting: an algebraic and logic approach
Handbook of theoretical computer science (vol. B)
Journal of Computer and System Sciences
A very hard log-space counting class
Theoretical Computer Science - Special issue on structure in complexity theory
Finite automata, formal logic, and circuit complexity
Finite automata, formal logic, and circuit complexity
On the complexity of bounded-variable queries (extended abstract)
PODS '95 Proceedings of the fourteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Succinct circuit representations and leaf language classes are basically the same concept
Information Processing Letters
Hierarchically specified unit disk graphs
Theoretical Computer Science
Handbook of formal languages, vol. 3
Languages, automata, and logic
Handbook of formal languages, vol. 3
Languages represented by Boolean formulas
Information Processing Letters
Approximation Algorithms for PSPACE-Hard Hierarchically and Periodically Specified Problems
SIAM Journal on Computing
Succinct representation, leaf languages, and projection reductions
Information and Computation
Journal of the ACM (JACM)
Modal and temporal properties of processes
Modal and temporal properties of processes
Model checking of hierarchical state machines
ACM Transactions on Programming Languages and Systems (TOPLAS)
Deciding first-order properties of locally tree-decomposable structures
Journal of the ACM (JACM)
Hyperedge Replacement: Grammars and Languages
Hyperedge Replacement: Grammars and Languages
The complexity of approximating pspace-complete problems for hierarchical specifications
Nordic Journal of Computing
How to Encode a Logical Structure by an OBDD
COCO '98 Proceedings of the Thirteenth Annual IEEE Conference on Computational Complexity
The complexity of relational query languages (Extended Abstract)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Existential second-order logic over graphs: Charting the tractability frontier
Journal of the ACM (JACM)
Elements Of Finite Model Theory (Texts in Theoretical Computer Science. An Eatcs Series)
Elements Of Finite Model Theory (Texts in Theoretical Computer Science. An Eatcs Series)
Analysis of recursive state machines
ACM Transactions on Programming Languages and Systems (TOPLAS)
Model-Checking Hierarchical Structures
LICS '05 Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
Relationships between nondeterministic and deterministic tape complexities
Journal of Computer and System Sciences
Fixpoint logics on hierarchical structures
FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
A comparison of succinctly represented finite-state systems
CONCUR'12 Proceedings of the 23rd international conference on Concurrency Theory
TACAS'13 Proceedings of the 19th international conference on Tools and Algorithms for the Construction and Analysis of Systems
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Hierarchical graph definitions allow a modular description of structures using modules for the specification of repeated substructures. Beside this modularity, hierarchical graph definitions allow us to specify structures of exponential size using polynomial size descriptions. In many cases, this succinctness increases the computational complexity of decision problems when input structures are defined hierarchically. In this paper, the model-checking problem for first-order logic (FO), monadic second-order logic (MSO), and second-order logic (SO) on hierarchically defined input structures is investigated. It is shown that in general these model-checking problems are exponentially harder than their non-hierarchical counterparts, where the input structures are given explicitly. As a consequence, several new complete problems for the levels of the polynomial time hierarchy and the exponential time hierarchy are obtained. Based on classical results of Gaifman and Courcelle, two restrictions on the structure of hierarchical graph definitions that lead to more efficient model-checking algorithms are presented.