143 research outputs found
Unified Analysis of Collapsible and Ordered Pushdown Automata via Term Rewriting
We model collapsible and ordered pushdown systems with term rewriting, by
encoding higher-order stacks and multiple stacks into trees. We show a uniform
inverse preservation of recognizability result for the resulting class of term
rewriting systems, which is obtained by extending the classic saturation-based
approach. This result subsumes and unifies similar analyses on collapsible and
ordered pushdown systems. Despite the rich literature on inverse preservation
of recognizability for term rewrite systems, our result does not seem to follow
from any previous study.Comment: in Proc. of FRE
Reachability analysis of first-order definable pushdown systems
We study pushdown systems where control states, stack alphabet, and
transition relation, instead of being finite, are first-order definable in a
fixed countably-infinite structure. We show that the reachability analysis can
be addressed with the well-known saturation technique for the wide class of
oligomorphic structures. Moreover, for the more restrictive homogeneous
structures, we are able to give concrete complexity upper bounds. We show ample
applicability of our technique by presenting several concrete examples of
homogeneous structures, subsuming, with optimal complexity, known results from
the literature. We show that infinitely many such examples of homogeneous
structures can be obtained with the classical wreath product construction.Comment: to appear in CSL'1
Weighted Pushdown Systems with Indexed Weight Domains
The reachability analysis of weighted pushdown systems is a very powerful
technique in verification and analysis of recursive programs. Each transition
rule of a weighted pushdown system is associated with an element of a bounded
semiring representing the weight of the rule. However, we have realized that
the restriction of the boundedness is too strict and the formulation of
weighted pushdown systems is not general enough for some applications. To
generalize weighted pushdown systems, we first introduce the notion of stack
signatures that summarize the effect of a computation of a pushdown system and
formulate pushdown systems as automata over the monoid of stack signatures. We
then generalize weighted pushdown systems by introducing semirings indexed by
the monoid and weaken the boundedness to local boundedness
Random Generation and Enumeration of Accessible Determinisitic Real-time Pushdown Automata
This papers presents a general framework for the uniform random generation of
deterministic real-time accessible pushdown automata. A polynomial time
algorithm to randomly generate a pushdown automaton having a fixed stack
operations total size is proposed. The influence of the accepting condition
(empty stack, final state) on the reachability of the generated automata is
investigated.Comment: Frank Drewes. CIAA 2015, Aug 2015, Umea, Sweden. Springer, 9223,
pp.12, 2015, Implementation and Application of Automata - 20th International
Conferenc
On undecidability results of real programming languages
Original article can be found at : http://www.vmars.tuwien.ac.at/ Copyright Institut fur Technische InformatikOften, it is argued that some problems in data-flow analysis such as e.g. worst case execution time analysis are undecidable (because the halting problem is) and therefore only a conservative approximation of the desired information is possible. In this paper, we show that the semantics for some important real programming languages – in particular those used for programming embedded devices – can be modeled as finite state systems or pushdown machines. This implies that the halting problem becomes decidable and therefore invalidates popular arguments for using conservative analysis
Zenoness for Timed Pushdown Automata
Timed pushdown automata are pushdown automata extended with a finite set of
real-valued clocks. Additionaly, each symbol in the stack is equipped with a
value representing its age. The enabledness of a transition may depend on the
values of the clocks and the age of the topmost symbol. Therefore, dense-timed
pushdown automata subsume both pushdown automata and timed automata. We have
previously shown that the reachability problem for this model is decidable. In
this paper, we study the zenoness problem and show that it is EXPTIME-complete.Comment: In Proceedings INFINITY 2013, arXiv:1402.661
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