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Many constraints restricting the result of some computations over an integersequence can be compactly represented by register automata. We improve thepropagation of the conjunction of such constraints on the same sequence bysynthesising a database of linear and non-linear invariants using theirregister-automaton representation. The obtained invariants are formulaeparameterised by a function of the sequence length and proven to be true forany long enough sequence. To assess the quality of such linear invariants, wedeveloped a method to verify whether a generated linear invariant is a facet ofthe convex hull of the feasible points. This method, as well as the proof ofnon-linear invariants, are based on the systematic generation of constant-sizedeterministic finite automata that accept all integer sequences whose resultverifies some simple condition. We apply such methodology to a set of 44time-series constraints and obtain 1400 linear invariants from which 70% arefacet defining, and 600 non-linear invariants, which were tested on short-termelectricity production problems.

Synthesising a Database of Parameterised Linear and Non-Linear Invariants for Time-Series Constraints