9 research outputs found
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
Recommended from our members
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
Recommended from our members
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
Behavioral validation in Cyber-physical systems: Safety violations and beyond
The advances in software and hardware technologies in the last two decades have paved the way for the development of complex systems we observe around us. Avionics, automotive, power grid, medical devices, and robotics are a few examples of such systems which are usually termed as Cyber-physical systems (CPS) as they often involve both physical and software components. Deployment of a CPS in a safety critical application mandates that the system operates reliably even in adverse scenarios. While effective in improving confidence in system functionality, testing can not ascertain the absence of failures; whereas, formal verification can be exhaustive but it may not scale well as the system complexity grows. Simulation driven analysis tends to bridge this gap by tapping key system properties from the simulations. Despite their differences, all these analyses can be pivotal in providing system behaviors as the evidence to the satisfaction or violation of a given performance specification. However, less attention has been paid to algorithmically validating and characterizing different behaviors of a CPS. The focus of this thesis is on behavioral validation of Cyber-physical systems, which can supplement an existing CPS analysis framework. This thesis develops algorithmic tools for validating verification artifacts by generating a variety of counterexamples for a safety violation in a linear hybrid system. These counterexamples can serve as performance metrics to evaluate different controllers during design and testing phases. This thesis introduces the notion of complete characterization of a safety violation in a linear system with bounded inputs, and it proposes a sound technique to compute and efficiently represent these characterizations. This thesis further presents neural network based frameworks to perform systematic state space exploration guided by sensitivity or its gradient approximation in learning-enabled control (LEC) systems. The presented technique is accompanied with convergence guarantees and yields considerable performance gain over a widely used falsification platform for a class of signal temporal logic (STL) specifications.Doctor of Philosoph