29,068 research outputs found
Sciduction: Combining Induction, Deduction, and Structure for Verification and Synthesis
Even with impressive advances in automated formal methods, certain problems
in system verification and synthesis remain challenging. Examples include the
verification of quantitative properties of software involving constraints on
timing and energy consumption, and the automatic synthesis of systems from
specifications. The major challenges include environment modeling,
incompleteness in specifications, and the complexity of underlying decision
problems.
This position paper proposes sciduction, an approach to tackle these
challenges by integrating inductive inference, deductive reasoning, and
structure hypotheses. Deductive reasoning, which leads from general rules or
concepts to conclusions about specific problem instances, includes techniques
such as logical inference and constraint solving. Inductive inference, which
generalizes from specific instances to yield a concept, includes algorithmic
learning from examples. Structure hypotheses are used to define the class of
artifacts, such as invariants or program fragments, generated during
verification or synthesis. Sciduction constrains inductive and deductive
reasoning using structure hypotheses, and actively combines inductive and
deductive reasoning: for instance, deductive techniques generate examples for
learning, and inductive reasoning is used to guide the deductive engines.
We illustrate this approach with three applications: (i) timing analysis of
software; (ii) synthesis of loop-free programs, and (iii) controller synthesis
for hybrid systems. Some future applications are also discussed
Estimating Treatment Effects using Neurosymbolic Program Synthesis
Estimating treatment effects from observational data is a central problem in
causal inference. Methods to solve this problem exploit inductive biases and
heuristics from causal inference to design multi-head neural network
architectures and regularizers. In this work, we propose to use neurosymbolic
program synthesis, a data-efficient, and interpretable technique, to solve the
treatment effect estimation problem. We theoretically show that neurosymbolic
programming can solve the treatment effect estimation problem. By designing a
Domain Specific Language (DSL) for treatment effect estimation problem based on
the inductive biases used in literature, we argue that neurosymbolic
programming is a better alternative to treatment effect estimation than
traditional methods. Our empirical study reveals that our method, which
implicitly encodes inductive biases in a DSL, achieves better performance on
benchmark datasets than the state-of-the-art methods.Comment: Preprin
From Perception to Programs: Regularize, Overparameterize, and Amortize
Toward combining inductive reasoning with perception abilities, we develop
techniques for neurosymbolic program synthesis where perceptual input is first
parsed by neural nets into a low-dimensional interpretable representation,
which is then processed by a synthesized program. We explore several techniques
for relaxing the problem and jointly learning all modules end-to-end with
gradient descent: multitask learning; amortized inference;
overparameterization; and a differentiable strategy for penalizing lengthy
programs. Collectedly this toolbox improves the stability of gradient-guided
program search, and suggests ways of learning both how to perceive input as
discrete abstractions, and how to symbolically process those abstractions as
programs.Comment: ICML 202
Are There Good Mistakes? A Theoretical Analysis of CEGIS
Counterexample-guided inductive synthesis CEGIS is used to synthesize
programs from a candidate space of programs. The technique is guaranteed to
terminate and synthesize the correct program if the space of candidate programs
is finite. But the technique may or may not terminate with the correct program
if the candidate space of programs is infinite. In this paper, we perform a
theoretical analysis of counterexample-guided inductive synthesis technique. We
investigate whether the set of candidate spaces for which the correct program
can be synthesized using CEGIS depends on the counterexamples used in inductive
synthesis, that is, whether there are good mistakes which would increase the
synthesis power. We investigate whether the use of minimal counterexamples
instead of arbitrary counterexamples expands the set of candidate spaces of
programs for which inductive synthesis can successfully synthesize a correct
program. We consider two kinds of counterexamples: minimal counterexamples and
history bounded counterexamples. The history bounded counterexample used in any
iteration of CEGIS is bounded by the examples used in previous iterations of
inductive synthesis. We examine the relative change in power of inductive
synthesis in both cases. We show that the synthesis technique using minimal
counterexamples MinCEGIS has the same synthesis power as CEGIS but the
synthesis technique using history bounded counterexamples HCEGIS has different
power than that of CEGIS, but none dominates the other.Comment: In Proceedings SYNT 2014, arXiv:1407.493
A Theory of Formal Synthesis via Inductive Learning
Formal synthesis is the process of generating a program satisfying a
high-level formal specification. In recent times, effective formal synthesis
methods have been proposed based on the use of inductive learning. We refer to
this class of methods that learn programs from examples as formal inductive
synthesis. In this paper, we present a theoretical framework for formal
inductive synthesis. We discuss how formal inductive synthesis differs from
traditional machine learning. We then describe oracle-guided inductive
synthesis (OGIS), a framework that captures a family of synthesizers that
operate by iteratively querying an oracle. An instance of OGIS that has had
much practical impact is counterexample-guided inductive synthesis (CEGIS). We
present a theoretical characterization of CEGIS for learning any program that
computes a recursive language. In particular, we analyze the relative power of
CEGIS variants where the types of counterexamples generated by the oracle
varies. We also consider the impact of bounded versus unbounded memory
available to the learning algorithm. In the special case where the universe of
candidate programs is finite, we relate the speed of convergence to the notion
of teaching dimension studied in machine learning theory. Altogether, the
results of the paper take a first step towards a theoretical foundation for the
emerging field of formal inductive synthesis
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