AbsSynthe: abstract synthesis from succinct safety specifications

In this paper, we describe a synthesis algorithm for safety specifications described as circuits. Our algorithm is based on fixpoint computations, abstraction and refinement, it uses binary decision diagrams as symbolic data structure. We evaluate our tool on the benchmarks provided by the organizers of the synthesis competition organized within the SYNT'14 workshop.Comment: In Proceedings SYNT 2014, arXiv:1407.493

SAT-Based Methods for Circuit Synthesis

Reactive synthesis supports designers by automatically constructing correct hardware from declarative specifications. Synthesis algorithms usually compute a strategy, and then construct a circuit that implements it. In this work, we study SAT- and QBF-based methods for the second step, i.e., computing circuits from strategies. This includes methods based on QBF-certification, interpolation, and computational learning. We present optimizations, efficient implementations, and experimental results for synthesis from safety specifications, where we outperform BDDs both regarding execution time and circuit size. This is an extended version of [2], with an additional appendix.Comment: Extended version of a paper at FMCAD'1

Efficient Symbolic Supervisory Synthesis and Guard Generation: Evaluating partitioning techniques for the state-space exploration

The supervisory control theory (SCT) is a model-based framework, which automatically synthesizes a supervisor that restricts a plant to be controlled based on specifications to be fulfilled. Two main problems, typically encountered in industrial applications, prevent SCT from having a major breakthrough. First, the supervisor which is synthesized automatically from the given plant and specification models might be incomprehensible to the users. To tackle this problem, an approach was recently presented to extract compact propositional formulae (guards) from the supervisor, represented symbolically by binary decision diagrams (BDD). These guards are then attached to the original models, which results in a modular and comprehensible representation of the supervisor. However, this approach, which computes the supervisor symbolically in the conjunctive way, might lead to another problem: the state-space explosion, because of the large number of intermediate BDD nodes during computation. To alleviate this problem, we introduce in this paper an alternative approach that is based on the disjunctive partitioning technique, including a set of selection heuristics. Then this approach is adapted to the guard generation procedure. Finally, the efficiency of the presented approach is demonstrated on a set of benchmark examples

SAT-Based Synthesis Methods for Safety Specs

Automatic synthesis of hardware components from declarative specifications is an ambitious endeavor in computer aided design. Existing synthesis algorithms are often implemented with Binary Decision Diagrams (BDDs), inheriting their scalability limitations. Instead of BDDs, we propose several new methods to synthesize finite-state systems from safety specifications using decision procedures for the satisfiability of quantified and unquantified Boolean formulas (SAT-, QBF- and EPR-solvers). The presented approaches are based on computational learning, templates, or reduction to first-order logic. We also present an efficient parallelization, and optimizations to utilize reachability information and incremental solving. Finally, we compare all methods in an extensive case study. Our new methods outperform BDDs and other existing work on some classes of benchmarks, and our parallelization achieves a super-linear speedup. This is an extended version of [5], featuring an additional appendix.Comment: Extended version of a paper at VMCAI'1

Sparse Positional Strategies for Safety Games

We consider the problem of obtaining sparse positional strategies for safety games. Such games are a commonly used model in many formal methods, as they make the interaction of a system with its environment explicit. Often, a winning strategy for one of the players is used as a certificate or as an artefact for further processing in the application. Small such certificates, i.e., strategies that can be written down very compactly, are typically preferred. For safety games, we only need to consider positional strategies. These map game positions of a player onto a move that is to be taken by the player whenever the play enters that position. For representing positional strategies compactly, a common goal is to minimize the number of positions for which a winning player's move needs to be defined such that the game is still won by the same player, without visiting a position with an undefined next move. We call winning strategies in which the next move is defined for few of the player's positions sparse. Unfortunately, even roughly approximating the density of the sparsest strategy for a safety game has been shown to be NP-hard. Thus, to obtain sparse strategies in practice, one either has to apply some heuristics, or use some exhaustive search technique, like ILP (integer linear programming) solving. In this paper, we perform a comparative study of currently available methods to obtain sparse winning strategies for the safety player in safety games. We consider techniques from common knowledge, such as using ILP or SAT (satisfiability) solving, and a novel technique based on iterative linear programming. The results of this paper tell us if current techniques are already scalable enough for practical use.Comment: In Proceedings SYNT 2012, arXiv:1207.055

Challenges in Synthesizing Fast Control-Dominated Circuits

Presenting designers with higher-level specification languages is one sure way to improve productivity, but the more abstract the language, the higher the compiler's optimization burden. We consider generating efficient controller circuits from descriptions written in Esterel. To understand the demands of scalable optimization algorithms, we manually matched the results from sequential synthesis algorithms that produce good circuits but are costly or impossible to run on large designs. We hoped the high-level structure of Esterel would suggest inexpensive, effective optimizations, but our results are mixed. In the five examples we considered, many optimizations clearly could be automated cheaply, but we needed more global information to match the quality of the existing automatic techniques. This suggests an effective solution would have to combine both local and (potentially costly) global techniques

Synthesizing and tuning chemical reaction networks with specified behaviours

We consider how to generate chemical reaction networks (CRNs) from functional specifications. We propose a two-stage approach that combines synthesis by satisfiability modulo theories and Markov chain Monte Carlo based optimisation. First, we identify candidate CRNs that have the possibility to produce correct computations for a given finite set of inputs. We then optimise the reaction rates of each CRN using a combination of stochastic search techniques applied to the chemical master equation, simultaneously improving the of correct behaviour and ruling out spurious solutions. In addition, we use techniques from continuous time Markov chain theory to study the expected termination time for each CRN. We illustrate our approach by identifying CRNs for majority decision-making and division computation, which includes the identification of both known and unknown networks.Comment: 17 pages, 6 figures, appeared the proceedings of the 21st conference on DNA Computing and Molecular Programming, 201