Many constraints restricting the result of some computations over an integer sequence can be compactly represented by counter automata. We improve the propagation of the conjunction of such constraints on the same sequence by synthesising a database of linear and non-linear invariants using their counter-automaton representation. The obtained invariants are formulae parameterised by the sequence length and proven to be true for any long enough sequence. To assess the quality of such linear invariants, we developed a method to verify whether a generated linear invariant is a facet of the convex hull of the feasible points. This method, as well as the proof of non-linear invariants, are based on the systematic generation of constant-size deterministic finite automata that accept all integer sequences whose result verifies some simple condition. We apply such methodology to a set of 44 time-series constraints and obtain 1400 linear invariants from which 70% are facet defining, and 600 non-linear invariants, which were tested on short-term electricity production problems.
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This is an extended version of the CP 2017 article . Ekaterina Arafailova is supported by the EU H2020 programme under grant 640954 for project GRACeFUL. Nicolas Beldiceanu is partially supported by the GRACeFUL project and by the Gaspard Monge Program for Optimisation and Operations Research (PGMO). Helmut Simonis is supported by Science Foundation Ireland (SFI) under grant SFI/10/IN.1/I3032; the Insight Centre for Data Analytics is supported by SFI under grant SFI/12/RC/2289.
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Arafailova, E., Beldiceanu, N. & Simonis, H. Invariants for time-series constraints. Constraints 25, 71–120 (2020). https://doi.org/10.1007/s10601-020-09308-z
- Register automaton
- Time-series constraints
- Linear invariant
- Non-linear invariant
- Parameterised invariant
- Finite automaton