76 research outputs found
Senescent ground tree rewrite systems
Ground Tree Rewrite Systems with State are known to have an undecidable
control state reachability problem. Taking inspiration from the recent
introduction of scope-bounded multi-stack pushdown systems, we define Senescent
Ground Tree Rewrite Systems. These are a restriction of ground tree rewrite
systems with state such that nodes of the tree may no longer be rewritten after
having witnessed an a priori fixed number of control state changes. As well as
generalising scope-bounded multi-stack pushdown systems, we show --- via
reductions to and from reset Petri-nets --- that these systems have an
Ackermann-complete control state reachability problem. However, reachability of
a regular set of trees remains undecidable
Complexity Hierarchies Beyond Elementary
We introduce a hierarchy of fast-growing complexity classes and show its
suitability for completeness statements of many non elementary problems. This
hierarchy allows the classification of many decision problems with a
non-elementary complexity, which occur naturally in logic, combinatorics,
formal languages, verification, etc., with complexities ranging from simple
towers of exponentials to Ackermannian and beyond.Comment: Version 3 is the published version in TOCT 8(1:3), 2016. I will keep
updating the catalogue of problems from Section 6 in future revision
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
Unboundedness and downward closures of higher-order pushdown automata
We show the diagonal problem for higher-order pushdown automata (HOPDA), and
hence the simultaneous unboundedness problem, is decidable. From recent work by
Zetzsche this means that we can construct the downward closure of the set of
words accepted by a given HOPDA. This also means we can construct the downward
closure of the Parikh image of a HOPDA. Both of these consequences play an
important role in verifying concurrent higher-order programs expressed as HOPDA
or safe higher-order recursion schemes
Senescence
The book "Senescence" is aimed to describe all the phenomena related to aging and senescence of all forms of life on Earth, i.e. plants, animals and the human beings. The book contains 36 carefully reviewed chapters written by different authors, aiming to describe the aging and senescent changes of living creatures, i.e. plants and animals
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