ALASCA: Reasoning in Quantified Linear Arithmetic
Author:
Korovin KonstantinORCID, Kovács LauraORCID, Reger Giles, Schoisswohl JohannesORCID, Voronkov Andrei
Abstract
AbstractAutomated reasoning is routinely used in the rigorous construction and analysis of complex systems. Among different theories, arithmetic stands out as one of the most frequently used and at the same time one of the most challenging in the presence of quantifiers and uninterpreted function symbols. First-order theorem provers perform very well on quantified problems due to the efficient superposition calculus, but support for arithmetic reasoning is limited to heuristic axioms. In this paper, we introduce the $$\textsc {Alasca}$$
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calculus that lifts superposition reasoning to the linear arithmetic domain. We show that $$\textsc {Alasca}$$
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is both sound and complete with respect to an axiomatisation of linear arithmetic. We implemented and evaluated $$\textsc {Alasca}$$
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using the Vampire theorem prover, solving many more challenging problems compared to state-of-the-art reasoners.
Publisher
Springer Nature Switzerland
Reference41 articles.
1. Alt, L., Blicha, M., Hyvärinen, A.E.J., Sharygina, N.: SolCMC: Solidity Compiler’s Model Checker. In: CAV, LNCS, vol. 13371, pp. 325–338, Springer (2022), https://doi.org/10.1007/978-3-031-13185-1_16 2. Andreotti, B., Barbosa, H., Fontaine, P., Schurr, H.J.: veriT at SMT-COMP 2022. https://smt-comp.github.io/2022/system-descriptions/veriT.pdf (2022) 3. Bachmair, L., Ganzinger, H.: Ordered Chaining Calculi for First-Order Theories of Transitive Relations. J. ACM 45(6), 1007–1049 (1998), https://doi.org/10.1145/293347.293352, https://doi.org/10.1145/293347.293352 4. Bachmair, L., Ganzinger, H.: Resolution Theorem Proving. In: Handbook of Automated Reasoning, pp. 19–99, Elsevier and MIT Press (2001), https://doi.org/10.1016/b978-044450813-3/50004-7 5. Barbosa, H., Barrett, C., Brain, M., Kremer, G., Lachnitt, H., Mohamed, A., Mohamed, M., Niemetz, A., Nötzli, A., Ozdemir, A., Preiner, M., Reynolds, A., Sheng, Y., Tinelli, C., , Zohar, Y.: CVC5 at the SMT Competition 2022. https://smt-comp.github.io/2022/system-descriptions/cvc5.pdf (2022)
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