8,223 research outputs found
Serializing the Parallelism in Parallel Communicating Pushdown Automata Systems
We consider parallel communicating pushdown automata systems (PCPA) and
define a property called known communication for it. We use this property to
prove that the power of a variant of PCPA, called returning centralized
parallel communicating pushdown automata (RCPCPA), is equivalent to that of
multi-head pushdown automata. The above result presents a new sub-class of
returning parallel communicating pushdown automata systems (RPCPA) called
simple-RPCPA and we show that it can be written as a finite intersection of
multi-head pushdown automata systems
Analyzing Timed Systems Using Tree Automata
Timed systems, such as timed automata, are usually analyzed using their
operational semantics on timed words. The classical region abstraction for
timed automata reduces them to (untimed) finite state automata with the same
time-abstract properties, such as state reachability. We propose a new
technique to analyze such timed systems using finite tree automata instead of
finite word automata. The main idea is to consider timed behaviors as graphs
with matching edges capturing timing constraints. When a family of graphs has
bounded tree-width, they can be interpreted in trees and MSO-definable
properties of such graphs can be checked using tree automata. The technique is
quite general and applies to many timed systems. In this paper, as an example,
we develop the technique on timed pushdown systems, which have recently
received considerable attention. Further, we also demonstrate how we can use it
on timed automata and timed multi-stack pushdown systems (with boundedness
restrictions)
Revisiting Underapproximate Reachability for Multipushdown Systems
Boolean programs with multiple recursive threads can be captured as pushdown
automata with multiple stacks. This model is Turing complete, and hence, one is
often interested in analyzing a restricted class that still captures useful
behaviors. In this paper, we propose a new class of bounded under
approximations for multi-pushdown systems, which subsumes most existing
classes. We develop an efficient algorithm for solving the under-approximate
reachability problem, which is based on efficient fix-point computations. We
implement it in our tool BHIM and illustrate its applicability by generating a
set of relevant benchmarks and examining its performance. As an additional
takeaway, BHIM solves the binary reachability problem in pushdown automata. To
show the versatility of our approach, we then extend our algorithm to the timed
setting and provide the first implementation that can handle timed
multi-pushdown automata with closed guards.Comment: 52 pages, Conference TACAS 202
Automata with Nested Pebbles Capture First-Order Logic with Transitive Closure
String languages recognizable in (deterministic) log-space are characterized
either by two-way (deterministic) multi-head automata, or following Immerman,
by first-order logic with (deterministic) transitive closure. Here we elaborate
this result, and match the number of heads to the arity of the transitive
closure. More precisely, first-order logic with k-ary deterministic transitive
closure has the same power as deterministic automata walking on their input
with k heads, additionally using a finite set of nested pebbles. This result is
valid for strings, ordered trees, and in general for families of graphs having
a fixed automaton that can be used to traverse the nodes of each of the graphs
in the family. Other examples of such families are grids, toruses, and
rectangular mazes. For nondeterministic automata, the logic is restricted to
positive occurrences of transitive closure.
The special case of k=1 for trees, shows that single-head deterministic
tree-walking automata with nested pebbles are characterized by first-order
logic with unary deterministic transitive closure. This refines our earlier
result that placed these automata between first-order and monadic second-order
logic on trees.Comment: Paper for Logical Methods in Computer Science, 27 pages, 1 figur
An Experiment in Ping-Pong Protocol Verification by Nondeterministic Pushdown Automata
An experiment is described that confirms the security of a well-studied class
of cryptographic protocols (Dolev-Yao intruder model) can be verified by
two-way nondeterministic pushdown automata (2NPDA). A nondeterministic pushdown
program checks whether the intersection of a regular language (the protocol to
verify) and a given Dyck language containing all canceling words is empty. If
it is not, an intruder can reveal secret messages sent between trusted users.
The verification is guaranteed to terminate in cubic time at most on a
2NPDA-simulator. The interpretive approach used in this experiment simplifies
the verification, by separating the nondeterministic pushdown logic and program
control, and makes it more predictable. We describe the interpretive approach
and the known transformational solutions, and show they share interesting
features. Also noteworthy is how abstract results from automata theory can
solve practical problems by programming language means.Comment: In Proceedings MARS/VPT 2018, arXiv:1803.0866
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