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The design of embedded systems is becoming continuously more complex such that efficient system-level design methods are becoming crucial. Recently, combined Answer Set Programming (ASP) and Quantifier Free Integer Difference Logic (QF-IDL) solving has been shown to be a promising approach in system synthesis. However, this approach still has several restrictions limiting its applicability. In the paper at hand, we propose a novel ASP modulo Theories (ASPmT) system synthesis approach, which (i) supports more sophisticated system models, (ii) tightly integrates the QF-IDL solving into the ASP solving, and (iii) makes use of partial assignment checking. As a result, more realistic systems are considered and an early exclusion of infeasible solutions improves the entire system synthesis.
The recent series 5 of the Answer Set Programming (ASP) system clingo provides generic means to enhance basic ASP with theory reasoning capabilities. We instantiate this framework with different forms of linear constraints and elaborate upon its formal properties. Given this, we discuss the respective implementations, and present techniques for using these constraints in a reactive context. More precisely, we introduce extensions to clingo with difference and linear constraints over integers and reals, respectively, and realize them in complementary ways. Finally, we empirically evaluate the resulting clingo derivatives clingo[dl] and clingo[lp] on common language fragments and contrast them to related ASP systems.