Shaded Tangles for the Design and Verification of Quantum Programs (Extended Abstract)

We give a scheme for interpreting shaded tangles as quantum programs, with the property that isotopic tangles yield equivalent programs. We analyze many known quantum programs in this way -- including entanglement manipulation and error correction -- and in each case present a fully-topological formal verification, yielding in several cases substantial new insight into how the program works. We also use our methods to identify several new or generalized procedures.Comment: In Proceedings QPL 2017, arXiv:1802.0973

Abstract verification and debugging of constraint logic programs

The technique of Abstract Interpretation [13] has allowed the development of sophisticated program analyses which are provably correct and practical. The semantic approximations produced by such analyses have been traditionally applied to optimization during program compilation. However, recently, novel and promising applications of semantic approximations have been proposed in the more general context of program verification and debugging [3],[10],[7]

Resilient Quantum Computation: Error Models and Thresholds

Recent research has demonstrated that quantum computers can solve certain types of problems substantially faster than the known classical algorithms. These problems include factoring integers and certain physics simulations. Practical quantum computation requires overcoming the problems of environmental noise and operational errors, problems which appear to be much more severe than in classical computation due to the inherent fragility of quantum superpositions involving many degrees of freedom. Here we show that arbitrarily accurate quantum computations are possible provided that the error per operation is below a threshold value. The result is obtained by combining quantum error-correction, fault tolerant state recovery, fault tolerant encoding of operations and concatenation. It holds under physically realistic assumptions on the errors.Comment: 19 pages in RevTex, many figures, the paper is also avalaible at http://qso.lanl.gov/qc

Some Applications of Coding Theory in Computational Complexity

Error-correcting codes and related combinatorial constructs play an important role in several recent (and old) results in computational complexity theory. In this paper we survey results on locally-testable and locally-decodable error-correcting codes, and their applications to complexity theory and to cryptography. Locally decodable codes are error-correcting codes with sub-linear time error-correcting algorithms. They are related to private information retrieval (a type of cryptographic protocol), and they are used in average-case complexity and to construct ``hard-core predicates'' for one-way permutations. Locally testable codes are error-correcting codes with sub-linear time error-detection algorithms, and they are the combinatorial core of probabilistically checkable proofs

Fault Localization in Multi-Threaded C Programs using Bounded Model Checking (extended version)

Software debugging is a very time-consuming process, which is even worse for multi-threaded programs, due to the non-deterministic behavior of thread-scheduling algorithms. However, the debugging time may be greatly reduced, if automatic methods are used for localizing faults. In this study, a new method for fault localization, in multi-threaded C programs, is proposed. It transforms a multi-threaded program into a corresponding sequential one and then uses a fault-diagnosis method suitable for this type of program, in order to localize faults. The code transformation is implemented with rules and context switch information from counterexamples, which are typically generated by bounded model checkers. Experimental results show that the proposed method is effective, in such a way that sequential fault-localization methods can be extended to multi-threaded programs.Comment: extended version of paper published at SBESC'1

Multilevel Contracts for Trusted Components

This article contributes to the design and the verification of trusted components and services. The contracts are declined at several levels to cover then different facets, such as component consistency, compatibility or correctness. The article introduces multilevel contracts and a design+verification process for handling and analysing these contracts in component models. The approach is implemented with the COSTO platform that supports the Kmelia component model. A case study illustrates the overall approach.Comment: In Proceedings WCSI 2010, arXiv:1010.233

Intelligent encoding and economical communication in the visual stream.

The theory of computational complexity is used to underpin a recent model of neocortical sensory processing. We argue that encoding into reconstruction networks is appealing for communicating agents using Hebbian learning and working on hard combinatorial problems, which are easy to verify. Computational definition of the concept of intelligence is provided. Simulations illustrate the idea

Software Verification and Graph Similarity for Automated Evaluation of Students' Assignments

In this paper we promote introducing software verification and control flow graph similarity measurement in automated evaluation of students' programs. We present a new grading framework that merges results obtained by combination of these two approaches with results obtained by automated testing, leading to improved quality and precision of automated grading. These two approaches are also useful in providing a comprehensible feedback that can help students to improve the quality of their programs We also present our corresponding tools that are publicly available and open source. The tools are based on LLVM low-level intermediate code representation, so they could be applied to a number of programming languages. Experimental evaluation of the proposed grading framework is performed on a corpus of university students' programs written in programming language C. Results of the experiments show that automatically generated grades are highly correlated with manually determined grades suggesting that the presented tools can find real-world applications in studying and grading