55 research outputs found
On the Error Resilience of Ordered Binary Decision Diagrams
Ordered Binary Decision Diagrams (OBDDs) are a data structure that is used in
an increasing number of fields of Computer Science (e.g., logic synthesis,
program verification, data mining, bioinformatics, and data protection) for
representing and manipulating discrete structures and Boolean functions. The
purpose of this paper is to study the error resilience of OBDDs and to design a
resilient version of this data structure, i.e., a self-repairing OBDD. In
particular, we describe some strategies that make reduced ordered OBDDs
resilient to errors in the indexes, that are associated to the input variables,
or in the pointers (i.e., OBDD edges) of the nodes. These strategies exploit
the inherent redundancy of the data structure, as well as the redundancy
introduced by its efficient implementations. The solutions we propose allow the
exact restoring of the original OBDD and are suitable to be applied to
classical software packages for the manipulation of OBDDs currently in use.
Another result of the paper is the definition of a new canonical OBDD model,
called {\em Index-resilient Reduced OBDD}, which guarantees that a node with a
faulty index has a reconstruction cost , where is the number of nodes
with corrupted index
Satisfiable Tseitin Formulas Are Hard for Nondeterministic Read-Once Branching Programs
We consider satisfiable Tseitin formulas TS_{G,c} based on d-regular expanders G with the absolute value of the second largest eigenvalue less than d/3. We prove that any nondeterministic read-once branching program (1-NBP) representing TS_{G,c} has size 2^{Omega(n)}, where n is the number of vertices in G. It extends the recent result by Itsykson at el. [STACS 2017] from OBDD to 1-NBP.
On the other hand it is easy to see that TS_{G,c} can be represented as a read-2 branching program (2-BP) of size O(n), as the negation of a nondeterministic read-once branching program (1-coNBP) of size O(n) and as a CNF formula of size O(n). Thus TS_{G,c} gives the best possible separations (up to a constant in the exponent) between
1-NBP and 2-BP, 1-NBP and 1-coNBP and between 1-NBP and CNF
Components' IMportance Measures for Initiating and Enabling events in Fault Tree Analysis
This report deals with the problem of determining the exact values of the importance indexes of basic events in case of both unavailability and frequency analysis of coherent and non-coherent fault trees. In particular a new method is described for determining the importance of enabling events in case of frequency analysis. Insights are given into the importance analysis implemented in the new software ASTRA 3.0 based on the Binary Decision Diagram approach with Labelled variables (LBDD). The analysis methods are also described with reference to modularised fault trees. Simple numerical examples are provided to clarify how the methods work. Proofs of the implemented equations are provided in Appendixes.JRC.DG.G.7-Traceability and vulnerability assessmen
Detecting Redundant CSS Rules in HTML5 Applications: A Tree-Rewriting Approach
HTML5 applications normally have a large set of CSS (Cascading Style Sheets)
rules for data display. Each CSS rule consists of a node selector (given in an
XPath-like query language) and a declaration block (assigning values to
selected nodes' display attributes). As web applications evolve, maintaining
CSS files can easily become problematic. Some CSS rules will be replaced by new
ones, but these obsolete (hence redundant) CSS rules often remain in the
applications. Not only does this "bloat" the applications, but it also
significantly increases web browsers' processing time. Most works on detecting
redundant CSS rules in HTML5 applications do not consider the dynamic behaviors
of HTML5 (specified in JavaScript); in fact, the only proposed method that
takes these into account is dynamic analysis (a.k.a. testing), which cannot
soundly prove redundancy of CSS rules. In this paper, we introduce an
abstraction of HTML5 applications based on monotonic tree-rewriting and study
its "redundancy problem". We establish the precise complexity of the problem
and various subproblems of practical importance (ranging from P to EXP). In
particular, our algorithm relies on an efficient reduction to an analysis of
symbolic pushdown systems (for which highly optimised solvers are available),
which yields a fast method for checking redundancy in practice. We implemented
our algorithm and demonstrated its efficacy in detecting redundant CSS rules in
HTML5 applications.Comment: 50 page
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