  Automatic static cost analysis infers information about the resources used by
programs without actually running them with concrete data, and presents such
information as functions of input data sizes. Most of the analysis tools for
logic programs (and other languages) are based on setting up recurrence
relations representing (bounds on) the computational cost of predicates, and
solving them to find closed-form functions that are equivalent to (or a bound
on) them. Such recurrence solving is a bottleneck in current tools: many of the
recurrences that arise during the analysis cannot be solved with current
solvers, such as Computer Algebra Systems (CASs), so that specific methods for
different classes of recurrences need to be developed. We address such a
challenge by developing a novel, general approach for solving arbitrary,
constrained recurrence relations, that uses machine-learning sparse regression
techniques to guess a candidate closed-form function, and a combination of an
SMT-solver and a CAS to check whether such function is actually a solution of
the recurrence. We have implemented a prototype and evaluated it with
recurrences generated by a cost analysis system (the one in CiaoPP). The
experimental results are quite promising, showing that our approach can find
closed-form solutions, in a reasonable time, for classes of recurrences that
cannot be solved by such a system, nor by current CASs.
