High-level Programming via Generalized Planning and LTL Synthesis

Abstract

We look at program synthesis where the aim is to automatically synthesize a controller that operates on data structures and from which a concrete program can be easily derived. We do not aim at a fully-automatic process or tool that produces a program meeting a given specification of the program’s behaviour. Rather, we aim at the design of a clear and well-founded approach for supporting programmers at the design and implementation phases. Concretely, we first show that a program synthesis task can be modeled as a generalized planning problem. This is done at an abstraction level where the involved data structures are seen as black-boxes that can be interfaced with actions and observations, the first corresponding to the operations and the second to the queries provided by the data structure. The abstraction level is high enough to capture intuitive and common assumptions as well as general and simple strategies used by programmers, and yet it contains sufficient structure to support the automated generation of concrete solutions (in the form of controllers). From such controllers and the use of standard data structures, an actual program in a general language like C++ or Python can be easily obtained. Then, we discuss how the resulting generalized planning problem can be reduced to an LTL synthesis problem, thus making available any LTL synthesis engine for obtaining the controllers. We illustrate the effectiveness of the approach on a series of examples.

Generalized Planning as Heuristic Search: A new planning search-space that leverages pointers over objects

“…A common approach for the offline computation of generalized plans is compiling the GP problem into another form of problem solving, and using an off-the-shelf solver to work out the compiled problem. With this regard, GP problems have been compiled into classical planning problems [52,34], conformant planning problems [40], LTL synthesis problems [53], FOND planning problems [54,6] or MAXSAT problems [8]. The compilation approach is appealing because it allows to leverage the latest advances of other well-founded scientific communities, with robust and scalable solvers.…”

“…As noted by previous work on GP, the aims of GP are connected to program synthesis [34,6,53,33]. Program synthesis is a task traditionally studied by the computer-aided verification community [55], and that aims the computation of programs such that they satisfy a given correctness specification [56,57,58].…”

“…Generalized planning is an umbrella term that refers to more general notions of planning [7]. This work builds on top of the inductive formalism for GP, where a GP problem is defined as a finite set of classical planning instances that share a common structure [5,53]. In this work we assume that the finite set of classical planning instances in a GP problem belong to the same domain.…”

Flexible FOND Planning with Explicit Fairness Assumptions

“…We finally tested FOND-ASP over the 7 problems considered in a recent approach to program synthesis over unbounded data structures (Bonet, De Giacomo, Geffner, Patrizi, & Rubin, 2020). Although the original specifications are in LTL, these can be all expressed in FOND + using different types of conditional fairness assumptions.…”

Iterative Depth-First Search for FOND Planning

“…In FOND planning, states are fully observable and actions may have nondeterministic effects (i.e., an action may generate a set of possible successor states). FOND planning is relevant for solving other related planning models, such as stochastic shortest path (SSP) planning (Bertsekas and Tsitsiklis 1991), planning for temporally extended goals (Patrizi, Lipovetzky, and Geffner 2013;Camacho et al 2017;Camacho and McIlraith 2019;Camacho et al 2018;De Giacomo and Rubin 2018;Brafman and De Giacomo 2019), and generalized planning (Hu and Giacomo 2011;Bonet et al 2017Bonet et al , 2020. Solutions for FOND planning can be characterized as strong policies which guarantee to achieve the goal condition in a finite number of steps, and strong cyclic policies which guarantee to lead only to states from which a goal condition is satisfiable in a finite number of steps (Cimatti et al 2003).…”