We propose an abstraction-refinement-based algorithm for the problem of verifying the safety of a camera-based autonomous system in a synthetic 3D-scene, based on the notion of interval images. An interval image is an abstract data structure that represents a set of images in a 3D-scene. We give a computer graphics style rendering algorithm to efficiently compute interval images from a given region. Our proposed abstraction-refinement algorithm leverages recent abstract interpretation tools for neural networks. We have implemented and evaluated the proposed technique on complex 3D-scenes, demonstrating its effectiveness and scalability in comparison with earlier techniques.

We consider the problem of verifying the safety of the trajectories of a camera-based autonomous vehicle in a given 3-D-scene. We give a procedure to verify that all trajectories starting from a given initial region reach a specified target region safely without colliding with obstacles on the way. We also give a prioritization-based falsification procedure that collects unsafe trajectories. Both our procedures are based on the key notion of image-invariant regions, which are regions within which the captured images are identical. We evaluate our methods on a model of an autonomous road-following drone in a variety of 3-D-scenes; our experimental results demonstrate the feasibility and benefits of our approach for both safety analysis and falsification.

In earlier work (LICS 2016), the authors introduced two-variable first-order logic supplemented by a binary relation that allows one to say that a letter appears between two positions. We found an effective algebraic criterion that is a necessary condition for definability in this logic, and conjectured that the criterion is also sufficient, although we proved this only in the case of two-letter alphabets. Here we prove the general conjecture. The proof is quite different from the arguments in the earlier work, and required the development of novel techniques concerning factorizations of words. We extend the results to binary relations specifying that a factor appears between two positions.

We study an extension of FO2[<], first-order logic interpreted in finite words, in which formulas are restricted to use only two variables. We adjoin to this language two-variable atomic formulas that say, 'the letter a appears between positions x and y'. This is, in a sense, the simplest property that is not expressible using only two variables.

This proceedings volume has the papers presented at the 30th annual conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010), held at the Institute of Mathematical Sciences (IMSc), Chennai, during 15–18 December 2010. The conference attracted 128 submissions from 35 countries in 6 continents, most of them of very high quality. We thank the authors who submitted for making this such a competitive conference. The PC succeeded in obtaining the help of 216 external reviewers, in all producing 400 referee reports which were of immeasurable help in deciding the 38 contributed papers which have made it to this publication.

We consider concurrent systems that can be modelled as $1$-safe Petri nets communicating through a fixed set of buffers (modelled as unbounded places). We identify a parameter $\ben$, which we call ``benefit depth'', formed from the communication graph between the buffers. We show that for our system model, the coverability and boundedness problems can be solved in polynomial space assuming $\ben$ to be a fixed parameter, that is, the space requirement is $f(\ben)p(n)$, where $f$ is an exponential function and $p$ is a polynomial in the size of the input. We then obtain similar complexity bounds for modelchecking a logic based on such counting properties. This means that systems that have sparse communication patterns can be analyzed more efficiently than using previously known algorithms for general Petri nets.

We define a model of labelled product systems of automata and explore its connections with process calculi and trace languages. Bisimilarity of labelled product systems is defined using a new definition of bisimulation with renaming. Concurrent mu-expressions are defined to describe labelled product systems. This leads to complete axiomatizations and algorithms for bisimulation and failure equivalence over labelled product systems, and for equality over recognizable trace languages