Efficient Symbolic Representations for Arithmetic Constraints in Verification

Received (received date) Revised (revised date) Communicated by Editor's name ABSTRACT In this paper we discuss eecient symbolic representations for innnite-state systems speciied using linear arithmetic constraints. We give algorithms for constructing nite automata which represent integer sets that satisfy linear constraints. These automata can represent either signed or unsigned integers and have a lower number of states compared to other similar approaches. We present eecient storage techniques for the transition function of the automata and extend the construction algorithms to formulas on both boolean and integer variables. We also derive conditions which guarantee that the precondition computations used in symbolic veriication algorithms do not cause an exponential increase in the automata size. We experimentally compare diierent symbolic representations by using them to verify non-trivial concurrent systems. Experimental results show that the symbolic representations based on our construction algorithms outperform the polyhedral representation used in Omega Library, and the automata representation used in LASH.