  Answer Set Programming (ASP) has emerged as a promising paradigm in knowledge
representation and automated reasoning owing to its ability to model hard
combinatorial problems from diverse domains in a natural way. Building on
advances in propositional SAT solving, the past two decades have witnessed the
emergence of well-engineered systems for solving the answer set satisfiability
problem, i.e., finding models or answer sets for a given answer set program. In
recent years, there has been growing interest in problems beyond
satisfiability, such as model counting, in the context of ASP. Akin to the
early days of propositional model counting, state-of-the-art exact answer set
counters do not scale well beyond small instances. Exact ASP counters struggle
with handling larger input formulas. The primary contribution of this paper is
a new ASP counting framework, called sharpASP, which counts answer sets
avoiding larger input formulas. This relies on an alternative way of defining
answer sets that allows for the lifting of key techniques developed in the
context of propositional model counting. Our extensive empirical analysis over
1470 benchmarks demonstrates significant performance gain over current
state-of-the-art exact answer set counters. Specifically, by using sharpASP, we
were able to solve 1062 benchmarks with PAR2 score of 3082 whereas using prior
state-of-the-art, we could only solve 895 benchmarks with a PAR2 score of 4205,
all other experimental conditions being the same.
