186 research outputs found
A Type-Directed Negation Elimination
In the modal mu-calculus, a formula is well-formed if each recursive variable
occurs underneath an even number of negations. By means of De Morgan's laws, it
is easy to transform any well-formed formula into an equivalent formula without
negations -- its negation normal form. Moreover, if the formula is of size n,
its negation normal form of is of the same size O(n). The full modal
mu-calculus and the negation normal form fragment are thus equally expressive
and concise.
In this paper we extend this result to the higher-order modal fixed point
logic (HFL), an extension of the modal mu-calculus with higher-order recursive
predicate transformers. We present a procedure that converts a formula into an
equivalent formula without negations of quadratic size in the worst case and of
linear size when the number of variables of the formula is fixed.Comment: In Proceedings FICS 2015, arXiv:1509.0282
The Largest Respectful Function
Respectful functions were introduced by Sangiorgi as a compositional tool to
formulate short and clear bisimulation proofs. Usually, the larger the
respectful function, the easier the bisimulation proof. In particular the
largest respectful function, defined as the pointwise union of all respectful
functions, has been shown to be very useful. We here provide an explicit and
constructive characterization of it
Completeness for a First-order Abstract Separation Logic
Existing work on theorem proving for the assertion language of separation
logic (SL) either focuses on abstract semantics which are not readily available
in most applications of program verification, or on concrete models for which
completeness is not possible. An important element in concrete SL is the
points-to predicate which denotes a singleton heap. SL with the points-to
predicate has been shown to be non-recursively enumerable. In this paper, we
develop a first-order SL, called FOASL, with an abstracted version of the
points-to predicate. We prove that FOASL is sound and complete with respect to
an abstract semantics, of which the standard SL semantics is an instance. We
also show that some reasoning principles involving the points-to predicate can
be approximated as FOASL theories, thus allowing our logic to be used for
reasoning about concrete program verification problems. We give some example
theories that are sound with respect to different variants of separation logics
from the literature, including those that are incompatible with Reynolds's
semantics. In the experiment we demonstrate our FOASL based theorem prover
which is able to handle a large fragment of separation logic with heap
semantics as well as non-standard semantics.Comment: This is an extended version of the APLAS 2016 paper with the same
titl
Automated verification of shape, size and bag properties.
In recent years, separation logic has emerged as a contender for formal reasoning of heap-manipulating imperative programs. Recent works have focused on specialised provers that are mostly based on fixed sets of predicates. To improve expressivity, we have proposed a prover that can automatically handle user-defined predicates. These shape predicates allow programmers to describe a wide range of data structures with their associated size properties. In the current work, we shall enhance this prover by providing support for a new type of constraints, namely bag (multi-set) constraints. With this extension, we can capture the reachable nodes (or values) inside a heap predicate as a bag constraint. Consequently, we are able to prove properties about the actual values stored inside a data structure
Lightweight Multilingual Software Analysis
Developer preferences, language capabilities and the persistence of older
languages contribute to the trend that large software codebases are often
multilingual, that is, written in more than one computer language. While
developers can leverage monolingual software development tools to build
software components, companies are faced with the problem of managing the
resultant large, multilingual codebases to address issues with security,
efficiency, and quality metrics. The key challenge is to address the opaque
nature of the language interoperability interface: one language calling
procedures in a second (which may call a third, or even back to the first),
resulting in a potentially tangled, inefficient and insecure codebase. An
architecture is proposed for lightweight static analysis of large multilingual
codebases: the MLSA architecture. Its modular and table-oriented structure
addresses the open-ended nature of multiple languages and language
interoperability APIs. We focus here as an application on the construction of
call-graphs that capture both inter-language and intra-language calls. The
algorithms for extracting multilingual call-graphs from codebases are
presented, and several examples of multilingual software engineering analysis
are discussed. The state of the implementation and testing of MLSA is
presented, and the implications for future work are discussed.Comment: 15 page
Decidability and Complexity of Tree Share Formulas
Fractional share models are used to reason about how multiple actors share ownership of resources. We examine the decidability and complexity of reasoning over the "tree share" model of Dockins et al. using first-order logic, or fragments thereof. We pinpoint a connection between the basic operations on trees union, intersection, and complement and countable atomless Boolean algebras, allowing us to obtain decidability with the precise complexity of both first-order and existential theories over the tree share model with the aforementioned operations. We establish a connection between the multiplication operation on trees and the theory of word equations, allowing us to derive the decidability of its existential theory and the undecidability of its full first-order theory. We prove that the full first-order theory over the model with both the Boolean operations and the restricted multiplication operation (with constants on the right hand side) is decidable via an embedding to tree-automatic structures
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