We demonstrate the feasibility of using the XSB tabled logic programming system as a programmable fixed-point engine for implementing efficient local model checkers. In particular, we present XMC, an XSB-based local model checker for a CCS-like value-passing language and the alternation-free fragment of the modal mu-calculus. XMC is written in under 200 lines of XSB code, which constitute a declarative specification of CCS and the modal mu-calculus at the level of semantic equations. In order to gauge the performance of XMC as an algorithmic model checker, we conducted a series of benchmarking experiments designed to compare the performance of XMC with the local model checkers implemented in C/C++ in the Concurrency Factory and SPIN specification and verification environments. After applying certain newly developed logic-programming-based optimizations (along with some standard ones), XMC's performance became extremely competitive with that of the Factory and shows promise in its comparison with SPIN.