Verification of parallel programs with input variables represents a significant and well-motivated challenge. This paper addresses the challenge with a verification method that combines explicit and symbolic approaches to the state space representation. The state matching between non-canonical representations proved to be the bottleneck of such a combination, since its computation entailed deciding satisfiability of quantified bit-vector formulae. This limitation is here addressed by an alternative state matching, based on quantifier-free, and a heuristics optimising the state space searching. The experimental evaluation shows that the alternative state matching causes only a minor increase in the number of states and that, in combination with the heuristics, it considerably extends the scope of applicability of the proposed LTL model checking.