Abstract Learning Frameworks for Synthesis

We develop abstract learning frameworks (ALFs) for synthesis that embody the principles of CEGIS (counter-example based inductive synthesis) strategies that have become widely applicable in recent years. Our framework defines a general abstract framework of iterative learning, based on a hypothesis space that captures the synthesized objects, a sample space that forms the space on which induction is performed, and a concept space that abstractly defines the semantics of the learning process. We show that a variety of synthesis algorithms in current literature can be embedded in this general framework. While studying these embeddings, we also generalize some of the synthesis problems these instances are of, resulting in new ways of looking at synthesis problems using learning. We also investigate convergence issues for the general framework, and exhibit three recipes for convergence in finite time. The first two recipes generalize current techniques for convergence used by existing synthesis engines. The third technique is a more involved technique of which we know of no existing instantiation, and we instantiate it to concrete synthesis problems

Lazy Abstraction-Based Controller Synthesis

We present lazy abstraction-based controller synthesis (ABCS) for continuous-time nonlinear dynamical systems against reach-avoid and safety specifications. State-of-the-art multi-layered ABCS pre-computes multiple finite-state abstractions of varying granularity and applies reactive synthesis to the coarsest abstraction whenever feasible, but adaptively considers finer abstractions when necessary. Lazy ABCS improves this technique by constructing abstractions on demand. Our insight is that the abstract transition relation only needs to be locally computed for a small set of frontier states at the precision currently required by the synthesis algorithm. We show that lazy ABCS can significantly outperform previous multi-layered ABCS algorithms: on standard benchmarks, lazy ABCS is more than 4 times faster

Automatic Derivation of Statistical Algorithms: The EM Family and Beyond

Machine learning has reached a point where many probabilistic methods can be understood as variations, extensions and combinations of a much smaller set of abstract themes, e.g., as different instances of the EM algorithm. This enables the systematic derivation of algorithms customized for different models. Here, we describe the AUTOBAYES system which takes a high-level statistical model specification, uses powerful symbolic techniques based on schema-based program synthesis and computer algebra to derive an efficient specialized algorithm for learning that model, and generates executable code implementing that algorithm. This capability is far beyond that of code collections such as Matlab toolboxes or even tools for model-independent optimization such as BUGS for Gibbs sampling: complex new algorithms can be generated without new programming, algorithms can be highly specialized and tightly crafted for the exact structure of the model and data, and efficient and commented code can be generated for different languages or systems. We present automatically-derived algorithms ranging from closed-form solutions of Bayesian textbook problems to recently-proposed EM algorithms for clustering, regression, and a multinomial form of PCA

Decidability and Synthesis of Abstract Inductive Invariants

Decidability and synthesis of inductive invariants ranging in a given domain play an important role in many software and hardware verification systems. We consider here inductive invariants belonging to an abstract domain $A$ as defined in abstract interpretation, namely, ensuring the existence of the best approximation in $A$ of any system property. In this setting, we study the decidability of the existence of abstract inductive invariants in $A$ of transition systems and their corresponding algorithmic synthesis. Our model relies on some general results which relate the existence of abstract inductive invariants with least fixed points of best correct approximations in $A$ of the transfer functions of transition systems and their completeness properties. This approach allows us to derive decidability and synthesis results for abstract inductive invariants which are applied to the well-known Kildall's constant propagation and Karr's affine equalities abstract domains. Moreover, we show that a recent general algorithm for synthesizing inductive invariants in domains of logical formulae can be systematically derived from our results and generalized to a range of algorithms for computing abstract inductive invariants

Synthesis from specifications : basic concepts

The need has evolved for a synthesis tool at the computer system level. SpecSyn is one such tool. Basically, it will view the world as a set of chips communicating via protocols. Thus, an abstract specification would get synthesized into a set of one or more interconnected chips. From that point, detail is added to each chip's specification until its structure is synthesized or it is determined that a prefabricated chip similar in functionality can be used.Features of such a tool include executable specifications from which to synthesize, constraint driven partitioning of the specifications into components (chips) and synthesis of interfaces between them, translation into VHDL and synthesis into VHDL structures of micro-architectural components, and the use of other tools (e.g. MILO, a micro-architecture and logic optimizer, and LES, a layout expert system) to evaluate the quality of the chip layout generated from VHDL description.A major component of SpecSyn is SpecCharts, a high level specification language amenable to system level synthesis, able to represent designs from system to register transfer levels. The language consists of a hierarchy of states, represented in combined graphical and textual form, at the same time catering to the expression of concurrent behavior and specification of constraints. With it we have specified several Intel chips as well as higher level systems, and have found it to be quite powerful and easy to use.SpecSyn will have a graphical interface, from which the user can at any time view or edit a SpecChart, translate to VHDL and simulate, view statistics provided by estimators (such as area, speed, and pins), store and retrieve SpecCharts, apply basic Spec Chart operations, as well as apply the partitioning algorithms or interface synthesizer. Providing access to a wide range of tools, having a single language represent the design throughout the synthesis process, and having user specified constraints allow the user to have varying amounts of control over the synthesis process

Quantitative Timed Analysis of Interactive Markov Chains

Abstract This paper presents new algorithms and accompanying tool support for analyzing interactive Markov chains (IMCs), a stochastic timed 1 1 2-player game in which delays are exponentially distributed. IMCs are compositional and act as semantic model for engineering for-malisms such as AADL and dynamic fault trees. We provide algorithms for determining the extremal expected time of reaching a set of states, and the long-run average of time spent in a set of states. The prototypical tool Imca supports these algorithms as well as the synthesis of ε-optimal piecewise constant timed policies for timed reachability objectives. Two case studies show the feasibility and scalability of the algorithms.