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A Conflict-Driven Solving Procedure for Poly-Power Constraints

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Abstract

This paper studies the satisfiability problem of poly-power constraints (conjunctions of poly-power equations and inequalities), in which poly-powers are univariate nonlinear functions that extend integer exponents of polynomials to real algebraic exponents. To solve the poly-power constraint, we present a sound and complete procedure that incorporates conflict-driven learning with the exclusion algorithm for isolating positive roots of poly-powers. Furthermore, we introduce a kind of optimal interval-splitting, based on the Stern–Brocot tree and on binary rational numbers respectively, so that the operands occurring in the execution are chosen to be as simple as possible. The solving procedure, thereby, turns out to be promisingly efficient on randomly generated examples.

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Acknowledgements

The authors thank the reviewers, whose careful and insightful comments improve the presentation of the paper and clarify inconsistencies significantly.

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Authors and Affiliations

  1. Shanghai Key Lab of Multidimensional Information Processing, East China Normal University, Shanghai, China

    Cheng-Chao Huang & Ming Xu

  2. Department of Computer Science and Technology, East China Normal University, Shanghai, China

    Cheng-Chao Huang, Ming Xu & Zhi-Bin Li

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  1. Cheng-Chao Huang
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  2. Ming Xu
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  3. Zhi-Bin Li
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Correspondence to Ming Xu.

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This work is funded by the National Natural Science Foundation of China (Nos. 11871221 and 11435005), the National Key R&D Program of China (No. 2018YFA0306704), and the Science and Technology Commission of Shanghai Municipality (No. 14DZ2260800).

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Huang, CC., Xu, M. & Li, ZB. A Conflict-Driven Solving Procedure for Poly-Power Constraints. J Autom Reasoning 64, 1–20 (2020). https://doi.org/10.1007/s10817-018-09501-z

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