Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Alternating automata, the weak monadic theory of the tree, and its complexity
International Colloquium on Automata, Languages and Programming on Automata, languages and programming
Handbook of theoretical computer science (vol. B)
A practical algorithm for exact array dependence analysis
Communications of the ACM
On syntactic congruences for &ohgr;-languages
Theoretical Computer Science - Special issue: formal language theory
On the Expressiveness of Real and Integer Arithmetic Automata (Extended Abstract)
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
On the Construction of Automata from Linear Arithmetic Constraints
TACAS '00 Proceedings of the 6th International Conference on Tools and Algorithms for Construction and Analysis of Systems: Held as Part of the European Joint Conferences on the Theory and Practice of Software, ETAPS 2000
An Automata-Theoretic Approach to Presburger Arithmetic Constraints (Extended Abstract)
SAS '95 Proceedings of the Second International Symposium on Static Analysis
Counting the Solutions of Presburger Equations without Enumerating Them
CIAA '01 Revised Papers from the 6th International Conference on Implementation and Application of Automata
Verifying Systems with Infinite but Regular State Spaces
CAV '98 Proceedings of the 10th International Conference on Computer Aided Verification
An Improved Reachability Analysis Method for Strongly Linear Hybrid Systems (Extended Abstract)
CAV '97 Proceedings of the 9th International Conference on Computer Aided Verification
Diophantine Equations, Presburger Arithmetic and Finite Automata
CAAP '96 Proceedings of the 21st International Colloquium on Trees in Algebra and Programming
Symbolic Verification with Periodic Sets
CAV '94 Proceedings of the 6th International Conference on Computer Aided Verification
On the Use of Weak Automata for Deciding Linear Arithmetic with Integer and Real Variables
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
Weak Alternating Automata Are Not That Weak
ISTCS '97 Proceedings of the Fifth Israel Symposium on the Theory of Computing Systems (ISTCS '97)
On the freeze quantifier in Constraint LTL: Decidability and complexity
Information and Computation
Bounded model checking of infinite state systems
Formal Methods in System Design
Bounds on the automata size for Presburger arithmetic
ACM Transactions on Computational Logic (TOCL)
Computing Convex Hulls by Automata Iteration
CIAA '08 Proceedings of the 13th international conference on Implementation and Applications of Automata
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
LATA '09 Proceedings of the 3rd International Conference on Language and Automata Theory and Applications
How to Tackle Integer Weighted Automata Positivity
RP '09 Proceedings of the 3rd International Workshop on Reachability Problems
Optimal metric planning with state sets in automata representation
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 2
Decompositions of grammar constraints
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 3
On the Use of Automata-based Techniques in Symbolic Model Checking
Electronic Notes in Theoretical Computer Science (ENTCS)
Decomposing global grammar constraints
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
On (Omega-)regular model checking
ACM Transactions on Computational Logic (TOCL)
Ehrenfeucht--Fraïssé goes automatic for real addition
Information and Computation
An evaluation of automata algorithms for string analysis
VMCAI'11 Proceedings of the 12th international conference on Verification, model checking, and abstract interpretation
Verification in predicate logic with time: algorithmic questions
CSL'05 Proceedings of the 19th international conference on Computer Science Logic
From automata to semilinear sets: a logical solution for sets L (C, P)
CIAA'04 Proceedings of the 9th international conference on Implementation and Application of Automata
On the satisfiability of modular arithmetic formulae
ATVA'06 Proceedings of the 4th international conference on Automated Technology for Verification and Analysis
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Linear numerical constraints and their first-order theory, whether defined over the reals or the integers, are basic tools that appear in many areas of Computer Science. This paper overviews a set of techniques based on finite automata that lead to decision procedures and other useful algorithms, as well as to a normal form, for the first-order linear theory of the integers, of the reals, and of the integers and reals combined. This approach has led to an implemented tool, which has the so far unique capability of handling the linear first-order theory of the integers and reals combined.