Meanders and their applications in lower bounds arguments
Journal of Computer and System Sciences - 27th IEEE Conference on Foundations of Computer Science October 27-29, 1986
Reduced order LQG controllers for linear time varying plants
Systems & Control Letters
Information Processing Letters
On the size of binary decision diagrams representing Boolean functions
Theoretical Computer Science
Communication complexity and parallel computing
Communication complexity and parallel computing
A Lower Bound for Integer Multiplication with Read-Once Branching Programs
SIAM Journal on Computing
To split or to conjoin: the question in image computation
Proceedings of the 37th Annual Design Automation Conference
Implicit enumeration of strongly connected components
ICCAD '99 Proceedings of the 1999 IEEE/ACM international conference on Computer-aided design
Symbolic Model Checking
Logic Synthesis and Verification Algorithms
Logic Synthesis and Verification Algorithms
A Symbolic Algorithms for Maximum Flow in 0-1 Networks
Formal Methods in System Design
Polynomial Formal Verification of Multipliers
Formal Methods in System Design
Computing strongly connected components in a linear number of symbolic steps
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
A Comparative Study of Symbolic Algorithms for the Computation of Fair Cycles
FMCAD '00 Proceedings of the Third International Conference on Formal Methods in Computer-Aided Design
An Algorithm for Strongly Connected Component Analysis in n log n Symbolic Steps
FMCAD '00 Proceedings of the Third International Conference on Formal Methods in Computer-Aided Design
New Bounds on the OBDD-Size of Integer Multiplication via Universal Hashing
STACS '01 Proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science
Efficient omega-Regular Language Containment
CAV '92 Proceedings of the Fourth International Workshop on Computer Aided Verification
Fine-Grain Conjunction Scheduling for Symbolic Reachability Analysis
TACAS '02 Proceedings of the 8th International Conference on Tools and Algorithms for the Construction and Analysis of Systems
CCC '02 Proceedings of the 17th IEEE Annual Conference on Computational Complexity
A lower bound for integer multiplication on randomized ordered read-once branching programs
Information and Computation
A symbolic approach to the all-pairs shortest-paths problem
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Lower bounds on the OBDD size of two fundamental functions' graphs
Information Processing Letters
A note on the size of OBDDs for the graph of integer multiplication
Information Processing Letters
Larger Lower Bounds on the OBDD Complexity of Integer Multiplication
LATA '09 Proceedings of the 3rd International Conference on Language and Automata Theory and Applications
Symbolic OBDD-Based Reachability Analysis Needs Exponential Space
SOFSEM '10 Proceedings of the 36th Conference on Current Trends in Theory and Practice of Computer Science
Exponential space complexity for OBDD-based reachability analysis
Information Processing Letters
Exponential space complexity for symbolic maximum flow algorithms in 0-1 networks
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Larger lower bounds on the OBDD complexity of integer multiplication
Information and Computation
On symbolic scheduling independent tasks with restricted execution times
WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
Exponential lower bounds on the space complexity of OBDD-Based graph algorithms
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
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Ordered binary decision diagrams (OBDDs) are a data structure for Boolean functions which supports many useful operations. It finds many applications in logic design, CAD, model checking, and symbolic graph algorithms. Nevertheless, many simple functions are known to have exponential OBDD size w. r. t. their number of variables. In order to investigate the limits of symbolic graph algorithms which work on OBDD-represented graph instances, it is useful to have simply-structured graphs whose OBDD representation has exponential size. Therefore, we consider fundamental arithmetic and storage access functions with exponential OBDD size and transfer these results to the graphs of these functions. Concretely, lower bounds for the graphs of integer multiplication, indirect storage access, and the hidden weighted bit function are presented. Finally, an exemplary application of the result for multiplication to the analysis of a symbolic all-pairs shortest-paths algorithm is sketched.