1,833 research outputs found
Data Multi-Pushdown Automata
We extend the classical model of multi-pushdown systems by considering systems that operate on a finite set of variables ranging over natural numbers. The conditions on variables are defined via gap-order constraints that allow to compare variables for equality, or to check that the gap between the values of two variables exceeds a given natural number. Furthermore, each message inside a stack is equipped with a data item representing its value. When a message is pushed to the stack, its value may be defined by a variable. When a message is popped, its value may be copied to a variable. Thus, we obtain a system that is infinite in multiple dimensions, namely we have a number of stacks that may contain an unbounded number of messages each of which is equipped with a natural number.
It is well-known that the verification of any non-trivial property of multi-pushdown systems is undecidable, even for two stacks and for a finite data-domain. In this paper, we show the decidability of the reachability problem for the classes of data multi-pushdown system that admit a bounded split-width (or equivalently a bounded tree-width). As an immediate consequence, we obtain decidability for several subclasses of data multi-pushdown systems. These include systems with single stacks, restricted ordering policies on stack operations, bounded scope, bounded phase, and bounded context switches
Model-Checking of Ordered Multi-Pushdown Automata
We address the verification problem of ordered multi-pushdown automata: A
multi-stack extension of pushdown automata that comes with a constraint on
stack transitions such that a pop can only be performed on the first non-empty
stack. First, we show that the emptiness problem for ordered multi-pushdown
automata is in 2ETIME. Then, we prove that, for an ordered multi-pushdown
automata, the set of all predecessors of a regular set of configurations is an
effectively constructible regular set. We exploit this result to solve the
global model-checking which consists in computing the set of all configurations
of an ordered multi-pushdown automaton that satisfy a given w-regular property
(expressible in linear-time temporal logics or the linear-time \mu-calculus).
As an immediate consequence, we obtain an 2ETIME upper bound for the
model-checking problem of w-regular properties for ordered multi-pushdown
automata (matching its lower-bound).Comment: 31 page
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
Multi-Head Finite Automata: Characterizations, Concepts and Open Problems
Multi-head finite automata were introduced in (Rabin, 1964) and (Rosenberg,
1966). Since that time, a vast literature on computational and descriptional
complexity issues on multi-head finite automata documenting the importance of
these devices has been developed. Although multi-head finite automata are a
simple concept, their computational behavior can be already very complex and
leads to undecidable or even non-semi-decidable problems on these devices such
as, for example, emptiness, finiteness, universality, equivalence, etc. These
strong negative results trigger the study of subclasses and alternative
characterizations of multi-head finite automata for a better understanding of
the nature of non-recursive trade-offs and, thus, the borderline between
decidable and undecidable problems. In the present paper, we tour a fragment of
this literature
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
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
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
Reachability for dynamic parametric processes
In a dynamic parametric process every subprocess may spawn arbitrarily many,
identical child processes, that may communicate either over global variables,
or over local variables that are shared with their parent.
We show that reachability for dynamic parametric processes is decidable under
mild assumptions. These assumptions are e.g. met if individual processes are
realized by pushdown systems, or even higher-order pushdown systems. We also
provide algorithms for subclasses of pushdown dynamic parametric processes,
with complexity ranging between NP and DEXPTIME.Comment: 31 page
Faster Algorithms for Weighted Recursive State Machines
Pushdown systems (PDSs) and recursive state machines (RSMs), which are
linearly equivalent, are standard models for interprocedural analysis. Yet RSMs
are more convenient as they (a) explicitly model function calls and returns,
and (b) specify many natural parameters for algorithmic analysis, e.g., the
number of entries and exits. We consider a general framework where RSM
transitions are labeled from a semiring and path properties are algebraic with
semiring operations, which can model, e.g., interprocedural reachability and
dataflow analysis problems.
Our main contributions are new algorithms for several fundamental problems.
As compared to a direct translation of RSMs to PDSs and the best-known existing
bounds of PDSs, our analysis algorithm improves the complexity for
finite-height semirings (that subsumes reachability and standard dataflow
properties). We further consider the problem of extracting distance values from
the representation structures computed by our algorithm, and give efficient
algorithms that distinguish the complexity of a one-time preprocessing from the
complexity of each individual query. Another advantage of our algorithm is that
our improvements carry over to the concurrent setting, where we improve the
best-known complexity for the context-bounded analysis of concurrent RSMs.
Finally, we provide a prototype implementation that gives a significant
speed-up on several benchmarks from the SLAM/SDV project
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