I/O efficient bisimulation partitioning on very large directed acyclic graphs

In this paper we introduce the first efficient external-memory algorithm to compute the bisimilarity equivalence classes of a directed acyclic graph (DAG). DAGs are commonly used to model data in a wide variety of practical applications, ranging from XML documents and data provenance models, to web taxonomies and scientific workflows. In the study of efficient reasoning over massive graphs, the notion of node bisimilarity plays a central role. For example, grouping together bisimilar nodes in an XML data set is the first step in many sophisticated approaches to building indexing data structures for efficient XPath query evaluation. To date, however, only internal-memory bisimulation algorithms have been investigated. As the size of real-world DAG data sets often exceeds available main memory, storage in external memory becomes necessary. Hence, there is a practical need for an efficient approach to computing bisimulation in external memory. Our general algorithm has a worst-case IO-complexity of O(Sort(|N| + |E|)), where |N| and |E| are the numbers of nodes and edges, resp., in the data graph and Sort(n) is the number of accesses to external memory needed to sort an input of size n. We also study specializations of this algorithm to common variations of bisimulation for tree-structured XML data sets. We empirically verify efficient performance of the algorithms on graphs and XML documents having billions of nodes and edges, and find that the algorithms can process such graphs efficiently even when very limited internal memory is available. The proposed algorithms are simple enough for practical implementation and use, and open the door for further study of external-memory bisimulation algorithms. To this end, the full open-source C++ implementation has been made freely available

Tools and Algorithms for the Construction and Analysis of Systems

This open access two-volume set constitutes the proceedings of the 26th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2020, which took place in Dublin, Ireland, in April 2020, and was held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The total of 60 regular papers presented in these volumes was carefully reviewed and selected from 155 submissions. The papers are organized in topical sections as follows: Part I: Program verification; SAT and SMT; Timed and Dynamical Systems; Verifying Concurrent Systems; Probabilistic Systems; Model Checking and Reachability; and Timed and Probabilistic Systems. Part II: Bisimulation; Verification and Efficiency; Logic and Proof; Tools and Case Studies; Games and Automata; and SV-COMP 2020

A formally verified compiler back-end

This article describes the development and formal verification (proof of semantic preservation) of a compiler back-end from Cminor (a simple imperative intermediate language) to PowerPC assembly code, using the Coq proof assistant both for programming the compiler and for proving its correctness. Such a verified compiler is useful in the context of formal methods applied to the certification of critical software: the verification of the compiler guarantees that the safety properties proved on the source code hold for the executable compiled code as well

Efficient external-memory bisimulation on DAGs

ABSTRACT In this paper we introduce the first efficient external-memory algorithm to compute the bisimilarity equivalence classes of a directed acyclic graph (DAG). DAGs are commonly used to model data in a wide variety of practical applications, ranging from XML documents and data provenance models, to web taxonomies and scientific workflows. In the study of efficient reasoning over massive graphs, the notion of node bisimilarity plays a central role. For example, grouping together bisimilar nodes in an XML data set is the first step in many sophisticated approaches to building indexing data structures for efficient XPath query evaluation. To date, however, only internal-memory bisimulation algorithms have been investigated. As the size of real-world DAG data sets often exceeds available main memory, storage in external memory becomes necessary. Hence, there is a practical need for an efficient approach to computing bisimulation in external memory. Our general algorithm has a worst-case IO-complexity of O(Sort(|N | + |E|)), where |N | and |E| are the numbers of nodes and edges, resp., in the data graph and Sort(n) is the number of accesses to external memory needed to sort an input of size n. We also study specializations of this algorithm to common variations of bisimulation for treestructured XML data sets. We empirically verify efficient performance of the algorithms on graphs and XML documents having billions of nodes and edges, and find that the algorithms can process such graphs efficiently even when very limited internal memory is available. The proposed algorithms are simple enough for practical implementation and use, and open the door for further study of externalmemory bisimulation algorithms. To this end, the full opensource C++ implementation has been made freely available

Translation validation for compilation verification

Modern optimizing compilers such as LLVM and GCC are huge and complex, and mature releases routinely have uncaught bugs. Beyond harm to software development, the lack of formal correctness guarantees for the compilation process seriously limits the guarantees other software systems can provide, since the compiler that generates the final executable cannot be trusted. These circumstances have motivated broad interest in compilation verification: providing a formal guarantee that a compilation of a program is correct. Translation Validation is a commonly used compilation verification technique that aims to prove the correctness of a single instance of compilation, by considering only the specific input and output programs and treating the compiler mostly as a black box. Translation Validation techniques are well-suited to the compilation verification problem because they can be composed to validate a sequence of compilation steps, they can easily retrofit to existing compilers, and they can be maintained independently from the compiler itself by a separate team of formal method experts. The basic components of a Translation Validation system are (1) a formal notion of program equivalence, (2) a verification condition generator that generates a relation between program points and variables in the input and output programs, (3) a proof system that accepts the verification conditions, generates a machine-checkable equivalence proof, and checks the proof for correctness. Ideally, such a system is completely agnostic to the specifics of transformation from the input to the output as well as independent of the input/output languages. This allows the same system to be reused across the many transformation and translation passes found in modern compilers. However, this is not true in the state of the art: most existing systems are custom-tailored for a particular sequence of transformations, and moreover, specialized for a specific, common intermediate language for the input and output programs. The overall goal of this work is to show that it is possible to develop a (mostly) language-independent, transformation-agnostic translation validation system with support for different input/output languages for an optimizing, production-quality compiler. In this thesis, we present such a system as well as the theoretical and practical advances needed to arrive to it. First, we present a formal framework for program equivalence checking that is transformation-agnostic and language-independent. This framework can serve as-is as the proof system for any number of Translation Validation systems targeting different transformation and/or translation phases within an existing compiler. The basis of the framework is a rigorous formalization, namely cut-bisimulation, for weak bisimulation variants that serve as a generalization of the various (sometimes ad-hoc) notions of program equivalence found in the literature. We develop a program equivalence checking algorithm that proves two programs equivalent by reducing a proposed relation between corresponding program states to a cut-bisimulation relation. We implement this algorithm in KEQ, a new tool for checking program equivalence that accepts the operational semantics of the input and output languages as parameters, and is independent of the transformation used to generate the output. This is the first program equivalence checking tool known to the authors that is language-parametric instead of containing hard-coded language semantics as is the norm in the literature. Then, we use KEQ as the equivalence checker for two different Translation Validation systems targeting two phases of the LLVM compiler: the Instruction Selection phase and the Register Allocation phase. The two systems share the same notion of equivalence (cut-bisimulation), the same proof system (KEQ), as well as the semantic definitions for the input/output languages (LLVM IR and x86-64 based Machine IR), which are separate artifacts and not hardcoded into the logic of the systems. The only components that are transformation-specific are the two verification condition generators. The Instruction Selection one requires minimal support from the compiler in the form of compiler-generated hints, while the Register Allocation one is employing a novel inference algorithm for register allocation and related optimizations. These systems were evaluated on the GCC SPEC 2006 benchmark, where they correctly validated 4331 / 4732 (91.52%) and 4574 / 4732 (96.67%) functions with supported features respectively

Programming Languages and Systems

This open access book constitutes the proceedings of the 29th European Symposium on Programming, ESOP 2020, which was planned to take place in Dublin, Ireland, in April 2020, as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The actual ETAPS 2020 meeting was postponed due to the Corona pandemic. The papers deal with fundamental issues in the specification, design, analysis, and implementation of programming languages and systems

Algebraic Pattern Matching in Join Calculus

We propose an extension of the join calculus with pattern matching on algebraic data types. Our initial motivation is twofold: to provide an intuitive semantics of the interaction between concurrency and pattern matching; to define a practical compilation scheme from extended join definitions into ordinary ones plus ML pattern matching. To assess the correctness of our compilation scheme, we develop a theory of the applied join calculus, a calculus with value passing and value matching. We implement this calculus as an extension of the current JoCaml system

DescribeX: A Framework for Exploring and Querying XML Web Collections

This thesis introduces DescribeX, a powerful framework that is capable of describing arbitrarily complex XML summaries of web collections, providing support for more efficient evaluation of XPath workloads. DescribeX permits the declarative description of document structure using all axes and language constructs in XPath, and generalizes many of the XML indexing and summarization approaches in the literature. DescribeX supports the construction of heterogeneous summaries where different document elements sharing a common structure can be declaratively defined and refined by means of path regular expressions on axes, or axis path regular expression (AxPREs). DescribeX can significantly help in the understanding of both the structure of complex, heterogeneous XML collections and the behaviour of XPath queries evaluated on them. Experimental results demonstrate the scalability of DescribeX summary refinements and stabilizations (the key enablers for tailoring summaries) with multi-gigabyte web collections. A comparative study suggests that using a DescribeX summary created from a given workload can produce query evaluation times orders of magnitude better than using existing summaries. DescribeX's light-weight approach of combining summaries with a file-at-a-time XPath processor can be a very competitive alternative, in terms of performance, to conventional fully-fledged XML query engines that provide DB-like functionality such as security, transaction processing, and native storage.Comment: PhD thesis, University of Toronto, 2008, 163 page

Programming Languages and Systems

This open access book constitutes the proceedings of the 28th European Symposium on Programming, ESOP 2019, which took place in Prague, Czech Republic, in April 2019, held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2019