Presburger arithmetic with unary predicates is P11 complete
Journal of Symbolic Logic
Theoretical Computer Science
How to Compose Presburger-Accelerations: Applications to Broadcast Protocols
FST TCS '02 Proceedings of the 22nd Conference Kanpur on Foundations of Software Technology and Theoretical Computer Science
Verifying Systems with Infinite but Regular State Spaces
CAV '98 Proceedings of the 10th International Conference on Computer Aided Verification
Superposition with Simplification as a Desision Procedure for the Monadic Class with Equality
KGC '93 Proceedings of the Third Kurt Gödel Colloquium on Computational Logic and Proof Theory
A General Method for Using Schematizations in Automated Deduction
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
Symbolic Verification with Periodic Sets
CAV '94 Proceedings of the 6th International Conference on Computer Aided Verification
Multiple Counters Automata, Safety Analysis and Presburger Arithmetic
CAV '98 Proceedings of the 10th International Conference on Computer Aided Verification
Resolution decision procedures
Handbook of automated reasoning
Flat Parametric Counter Automata
Fundamenta Informaticae - Machines, Computations and Universality, Part II
TACAS'08/ETAPS'08 Proceedings of the Theory and practice of software, 14th international conference on Tools and algorithms for the construction and analysis of systems
Superposition modulo linear arithmetic SUP(LA)
FroCoS'09 Proceedings of the 7th international conference on Frontiers of combining systems
Superposition-based analysis of first-order probabilistic timed automata
LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
Tree automata with equality constraints modulo equational theories
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Fast acceleration of ultimately periodic relations
CAV'10 Proceedings of the 22nd international conference on Computer Aided Verification
Integrating linear arithmetic into superposition calculus
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
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The hierarchic combination of linear arithmetic and first-order logic with free function symbols, FOL(LA), results in a strictly more expressive logic than its two parts. The SUP(LA) calculus can be turned into a decision procedure for interesting fragments of FOL(LA). For example, reachability problems for timed automata can be decided by SUP(LA) using an appropriate translation into FOL(LA). In this paper, we extend the SUP(LA) calculus with an additional inference rule, automatically generating inductive invariants from partial SUP(LA) derivations. The rule enables decidability of more expressive fragments, including reachability for timed automata with unbounded integer variables. We have implemented the rule in the SPASS(LA) theorem prover with promising results, showing that it can considerably speed up proof search and enable termination of saturation for practically relevant problems.