Synthesising a Database of Parameterised Linear and Non-Linear
  Invariants for Time-Series Constraints
  Many constraints restricting the result of some computations over an integer
sequence can be compactly represented by register 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
register-automaton representation. The obtained invariants are formulae
parameterised by a function of 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.
