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.

计数器自动机可以紧凑地表示许多限制整数序列上某些计算结果的约束。我们通过使用反自动机表示来合成线性和非线性不变量的数据库，从而改善了这些约束在同一序列上的并合传播。所获得的不变量是由序列长度参数化的公式，并证明对于任何足够长的序列都是正确的。为了评估此类线性不变量的质量，我们开发了一种方法来验证生成的线性不变量是否为可行点凸包的小平面。此方法以及非线性不变性的证明均基于系统生成的恒定大小确定性有限自动机，该自动机接受所有整数序列，其结果验证了一些简单条件。