Automatic verification of finite-state concurrent systems using temporal logic specifications
ACM Transactions on Programming Languages and Systems (TOPLAS)
Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Symbolic Boolean manipulation with ordered binary-decision diagrams
ACM Computing Surveys (CSUR)
Algebraic decision diagrams and their applications
ICCAD '93 Proceedings of the 1993 IEEE/ACM international conference on Computer-aided design
Logic in computer science: modelling and reasoning about systems
Logic in computer science: modelling and reasoning about systems
Model checking
Composite model-checking: verification with type-specific symbolic representations
ACM Transactions on Software Engineering and Methodology (TOSEM)
Branching programs and binary decision diagrams: theory and applications
Branching programs and binary decision diagrams: theory and applications
Efficient Detection of Vacuity in Temporal Model Checking
Formal Methods in System Design - Special issue on CAV '97
A framework for multi-valued reasoning over inconsistent viewpoints
ICSE '01 Proceedings of the 23rd International Conference on Software Engineering
Symbolic Model Checking
Multiway Decision Graphs for Automated Hardware Verification
Formal Methods in System Design
Arithmetic Boolean Expression Manipulator Using BDDs
Formal Methods in System Design
Multi-Terminal Binary Decision Diagrams: An Efficient DataStructure for Matrix Representation
Formal Methods in System Design
A Performance Study of BDD-Based Model Checking
FMCAD '98 Proceedings of the Second International Conference on Formal Methods in Computer-Aided Design
Implementing a Multi-valued Symbolic Model Checker
TACAS 2001 Proceedings of the 7th International Conference on Tools and Algorithms for the Construction and Analysis of Systems
Static Program Analysis via 3-Valued Logic
SAS '02 Proceedings of the 9th International Symposium on Static Analysis
CAV '00 Proceedings of the 12th International Conference on Computer Aided Verification
chi-Chek: A Multi-valued Model-Checker
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
Automatic Abstraction Using Generalized Model Checking
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
Boolean and Cartesian Abstraction for Model Checking C Programs
TACAS 2001 Proceedings of the 7th International Conference on Tools and Algorithms for the Construction and Analysis of Systems
A method to represent multiple-output switching functions by using multi-valued decision diagrams
ISMVL '96 Proceedings of the 26th International Symposium on Multiple-Valued Logic
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
Multi-valued symbolic model-checking
ACM Transactions on Software Engineering and Methodology (TOSEM)
Temporal Logic Query Checking: A Tool for Model Exploration
IEEE Transactions on Software Engineering
Systematic construction of abstractions for model-checking
VMCAI'06 Proceedings of the 7th international conference on Verification, Model Checking, and Abstract Interpretation
A Direct Algorithm for Multi-valued Bounded Model Checking
ATVA '08 Proceedings of the 6th International Symposium on Automated Technology for Verification and Analysis
Simulation for lattice-valued doubly labeled transition systems
International Journal of Approximate Reasoning
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Multi-valued logics provide an interesting alternative to classical boolean logic for modeling and reasoning about systems. Such logics can be used for reasoning about partially-specified systems, effectively encode vacuity detection and query-checking problems, help in detecting inconsistencies, and many others.In our earlier work, we identified a useful family of multi-valued logics: those specified over finite distributive lattices where negation preserves involution, i.e., $${{\neg}}{{\neg}} a = a$$ for every element a of the logic. Such structures are called quasi-boolean algebras, and model-checking over these not only extends the domain of applicability of automated reasoning to new problems, but can also speed up solutions to some classical verification problems.Symbolic model-checking over quasi-boolean algebras can be cast in terms of operations over multi-valued sets: sets whose membership functions are multi-valued. In this paper, we propose and empirically evaluate several choices for implementing multi-valued sets with decision diagrams. In particular, we describe two major approaches: (1) representing the multi-valued membership function canonically, using MDDs or ADDs; (2) representing multi-valued sets as a collection of classical sets, using a vector of either MBTDDs or BDDs. The naive implementation of (2) includes having a classical set for each value of the algebra. We exploit a result of lattice theory to reduce the number of such sets that need to be represented.The major contribution of this paper is the evaluation of the different implementations of multi-valued sets, done via a series of experiments and using several case studies.