On Reachability Analysis of Pushdown Systems with Transductions: Application to Boolean Programs with Call-by-Reference

Pushdown systems with transductions (TrPDSs) are an extension of pushdown systems (PDSs) by associating each transition rule with a transduction, which allows to inspect and modify the stack content at each step of a transition rule. It was shown by Uezato and Minamide that TrPDSs can model PDSs with checkpoint and discrete-timed PDSs. Moreover, TrPDSs can be simulated by PDSs and the predecessor configurations pre^*(C) of a regular set C of configurations can be computed by a saturation procedure when the closure of the transductions in TrPDSs is finite. In this work, we comprehensively investigate the reachability problem of finite TrPDSs. We propose a novel saturation procedure to compute pre^*(C) for finite TrPDSs. Also, we introduce a saturation procedure to compute the successor configurations post^*(C) of a regular set C of configurations for finite TrPDSs. From these two saturation procedures, we present two efficient implementation algorithms to compute pre^*(C) and post^*(C). Finally, we show how the presence of transductions enables the modeling of Boolean programs with call-by-reference parameter passing. The TrPDS model has finite closure of transductions which results in model-checking approach for Boolean programs with call-by-reference parameter passing against safety properties

Generalizing input-driven languages: theoretical and practical benefits

Regular languages (RL) are the simplest family in Chomsky's hierarchy. Thanks to their simplicity they enjoy various nice algebraic and logic properties that have been successfully exploited in many application fields. Practically all of their related problems are decidable, so that they support automatic verification algorithms. Also, they can be recognized in real-time. Context-free languages (CFL) are another major family well-suited to formalize programming, natural, and many other classes of languages; their increased generative power w.r.t. RL, however, causes the loss of several closure properties and of the decidability of important problems; furthermore they need complex parsing algorithms. Thus, various subclasses thereof have been defined with different goals, spanning from efficient, deterministic parsing to closure properties, logic characterization and automatic verification techniques. Among CFL subclasses, so-called structured ones, i.e., those where the typical tree-structure is visible in the sentences, exhibit many of the algebraic and logic properties of RL, whereas deterministic CFL have been thoroughly exploited in compiler construction and other application fields. After surveying and comparing the main properties of those various language families, we go back to operator precedence languages (OPL), an old family through which R. Floyd pioneered deterministic parsing, and we show that they offer unexpected properties in two fields so far investigated in totally independent ways: they enable parsing parallelization in a more effective way than traditional sequential parsers, and exhibit the same algebraic and logic properties so far obtained only for less expressive language families

Bounded Expectations: Resource Analysis for Probabilistic Programs

This paper presents a new static analysis for deriving upper bounds on the expected resource consumption of probabilistic programs. The analysis is fully automatic and derives symbolic bounds that are multivariate polynomials of the inputs. The new technique combines manual state-of-the-art reasoning techniques for probabilistic programs with an effective method for automatic resource-bound analysis of deterministic programs. It can be seen as both, an extension of automatic amortized resource analysis (AARA) to probabilistic programs and an automation of manual reasoning for probabilistic programs that is based on weakest preconditions. As a result, bound inference can be reduced to off-the-shelf LP solving in many cases and automatically-derived bounds can be interactively extended with standard program logics if the automation fails. Building on existing work, the soundness of the analysis is proved with respect to an operational semantics that is based on Markov decision processes. The effectiveness of the technique is demonstrated with a prototype implementation that is used to automatically analyze 39 challenging probabilistic programs and randomized algorithms. Experimental results indicate that the derived constant factors in the bounds are very precise and even optimal for many programs

Doctor of Philosophy

dissertationIn the static analysis of functional programs, control- ow analysis (k-CFA) is a classic method of approximating program behavior as a infinite state automata. CFA2 and abstract garbage collection are two recent, yet orthogonal improvements, on k-CFA. CFA2 approximates program behavior as a pushdown system, using summarization for the stack. CFA2 can accurately approximate arbitrarily-deep recursive function calls, whereas k-CFA cannot. Abstract garbage collection removes unreachable values from the store/heap. If unreachable values are not removed from a static analysis, they can become reachable again, which pollutes the final analysis and makes it less precise. Unfortunately, as these two techniques were originally formulated, they are incompatible. CFA2's summarization technique for managing the stack obscures the stack such that abstract garbage collection is unable to examine the stack for reachable values. This dissertation presents introspective pushdown control-flow analysis, which manages the stack explicitly through stack changes (pushes and pops). Because this analysis is able to examine the stack by how it has changed, abstract garbage collection is able to examine the stack for reachable values. Thus, introspective pushdown control-flow analysis merges successfully the benefits of CFA2 and abstract garbage collection to create a more precise static analysis. Additionally, the high-performance computing community has viewed functional programming techniques and tools as lacking the efficiency necessary for their applications. Nebo is a declarative domain-specific language embedded in C++ for discretizing partial differential equations for transport phenomena. For efficient execution, Nebo exploits a version of expression templates, based on the C++ template system, which is a type-less, completely-pure, Turing-complete functional language with burdensome syntax. Nebo's declarative syntax supports functional tools, such as point-wise lifting of complex expressions and functional composition of stencil operators. Nebo's primary abstraction is mathematical assignment, which separates what a calculation does from how that calculation is executed. Currently Nebo supports single-core execution, multicore (thread-based) parallel execution, and GPU execution. With single-core execution, Nebo performs on par with the loops and code that it replaces in Wasatch, a pre-existing high-performance simulation project. With multicore (thread-based) execution, Nebo can linearly scale (with roughly 90% efficiency) up to 6 processors, compared to its single-core execution. Moreover, Nebo's GPU execution can be up to 37x faster than its single-core execution. Finally, Wasatch (the pre-existing high-performance simulation project which uses Nebo) can scale up to 262K cores

Pushdown automata in statistical machine translation

This article describes the use of pushdown automata (PDA) in the context of statistical machine translation and alignment under a synchronous context-free grammar. We use PDAs to compactly represent the space of candidate translations generated by the grammar when applied to an input sentence. General-purpose PDA algorithms for replacement, composition, shortest path, and expansion are presented. We describe HiPDT, a hierarchical phrase-based decoder using the PDA representation and these algorithms. We contrast the complexity of this decoder with a decoder based on a finite state automata representation, showing that PDAs provide a more suitable framework to achieve exact decoding for larger synchronous context-free grammars and smaller language models. We assess this experimentally on a large-scale Chinese-to-English alignment and translation task. In translation, we propose a two-pass decoding strategy involving a weaker language model in the first-pass to address the results of PDA complexity analysis. We study in depth the experimental conditions and tradeoffs in which HiPDT can achieve state-of-the-art performance for large-scale SMT. </jats:p