No abstract

Rantanplan is a numeric planning solver that takes advantage of recent advances in SMT. It extends reduction to SAT approaches with an easy and efficient handling of numeric fluents using background theories. In this paper we describe the design choices and features of Rantanplan, especially, how numeric reasoning is integrated in the system. We also provide experimental results showing that Rantanplan is competitive with existing exact numeric planners.

Planning Modulo Theories (PMT), inspired by Satisfiability Modulo Theories (SMT), allows the integration of arbitrary first order theories, such as linear arithmetic, with propositional planning. Under this setting, planning as SAT is generalized to planning as SMT. In this paper we introduce a new encoding for planning as SMT, which adheres to the relaxed relaxed ∃-step (R 2 ∃-step) semantics for parallel plans. We show the benefits of relaxing the requirements on the set of actions eligible to be executed at the same time, even though many redundant actions can be introduced. We also show how, by a MaxSMT based post-processing step, redundant actions can be efficiently removed, and provide experimental results showing the benefits of this approach.

Pen and paper puzzles like Sudoku, Futoshiki and Skyscrapers are hugely popular. Solving such puzzles can be a trivial task for modern AI systems. However, most AI systems solve problems using a form of backtracking, while people try to avoid backtracking as much as possible. This means that existing AI systems do not output explanations about their reasoning that are meaningful to people. We present DEMYSTIFY, a tool which allows puzzles to be expressed in a high-level constraint programming language and uses MUSes to allow us to produce descriptions of steps in the puzzle solving. We give several improvements to the existing techniques for solving puzzles with MUSes, which allow us to solve a range of significantly more complex puzzles and give higher quality explanations. We demonstrate the effectiveness and generality of DEMYSTIFY by comparing its results to documented strategies for solving a range of pen and paper puzzles by hand, showing that our technique can find many of the same explanations.

Satisfiability Modulo Theories (SMT) is a well-established methodology that generalises propositional satisfiability (SAT) by adding support for a variety of theories such as integer arithmetic and bit-vector operations. SMT solvers have made rapid progress in recent years. In part, the efficiency of modern SMT solvers derives from the use of specialised decision procedures for each theory. In this paper we explore how the Essence Prime constraint modelling language can be translated to the standard SMT-LIB language. We target four theories: bit-vectors (QF BV), linear integer arithmetic (QF LIA), non-linear integer arithmetic (QF NIA), and integer difference logic (QF IDL). The encodings are implemented in the constraint modelling tool Savile Row. In an extensive set of experiments, we compare our encodings for the four theories, showing some notable differences and complementary strengths. We also compare our new encodings to the existing work targeting SMT and SAT, and to a well-established learning CP solver. Our two proposed encodings targeting the theory of bit-vectors (QF BV) both substantially outperform earlier work on encoding to QF BV on a large and diverse set of problem classes.