19 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
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
Pushdown reachability with constant treewidth
We consider the problem of reachability in pushdown graphs. We study the problem for pushdown graphs with constant treewidth. Even for pushdown graphs with treewidth 1, for the reachability problem we establish the following: (i) the problem is PTIME-complete, and (ii) any subcubic algorithm for the problem would contradict the k-clique conjecture and imply faster combinatorial algorithms for cliques in graphs
Parikh Image of Pushdown Automata
We compare pushdown automata (PDAs for short) against other representations.
First, we show that there is a family of PDAs over a unary alphabet with
states and stack symbols that accepts one single long word for
which every equivalent context-free grammar needs
variables. This family shows that the classical algorithm for converting a PDA
to an equivalent context-free grammar is optimal even when the alphabet is
unary. Moreover, we observe that language equivalence and Parikh equivalence,
which ignores the ordering between symbols, coincide for this family. We
conclude that, when assuming this weaker equivalence, the conversion algorithm
is also optimal. Second, Parikh's theorem motivates the comparison of PDAs
against finite state automata. In particular, the same family of unary PDAs
gives a lower bound on the number of states of every Parikh-equivalent finite
state automaton. Finally, we look into the case of unary deterministic PDAs. We
show a new construction converting a unary deterministic PDA into an equivalent
context-free grammar that achieves best known bounds.Comment: 17 pages, 2 figure
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
CFA2: a Context-Free Approach to Control-Flow Analysis
In a functional language, the dominant control-flow mechanism is function
call and return. Most higher-order flow analyses, including k-CFA, do not
handle call and return well: they remember only a bounded number of pending
calls because they approximate programs with control-flow graphs. Call/return
mismatch introduces precision-degrading spurious control-flow paths and
increases the analysis time. We describe CFA2, the first flow analysis with
precise call/return matching in the presence of higher-order functions and tail
calls. We formulate CFA2 as an abstract interpretation of programs in
continuation-passing style and describe a sound and complete summarization
algorithm for our abstract semantics. A preliminary evaluation shows that CFA2
gives more accurate data-flow information than 0CFA and 1CFA.Comment: LMCS 7 (2:3) 201