5,479 research outputs found
An Automaton Learning Approach to Solving Safety Games over Infinite Graphs
We propose a method to construct finite-state reactive controllers for
systems whose interactions with their adversarial environment are modeled by
infinite-duration two-player games over (possibly) infinite graphs. The
proposed method targets safety games with infinitely many states or with such a
large number of states that it would be impractical---if not impossible---for
conventional synthesis techniques that work on the entire state space. We
resort to constructing finite-state controllers for such systems through an
automata learning approach, utilizing a symbolic representation of the
underlying game that is based on finite automata. Throughout the learning
process, the learner maintains an approximation of the winning region
(represented as a finite automaton) and refines it using different types of
counterexamples provided by the teacher until a satisfactory controller can be
derived (if one exists). We present a symbolic representation of safety games
(inspired by regular model checking), propose implementations of the learner
and teacher, and evaluate their performance on examples motivated by robotic
motion planning in dynamic environments
Symbolic Automata with Memory: a Computational Model for Complex Event Processing
We propose an automaton model which is a combination of symbolic and register
automata, i.e., we enrich symbolic automata with memory. We call such automata
Register Match Automata (RMA). RMA extend the expressive power of symbolic
automata, by allowing formulas to be applied not only to the last element read
from the input string, but to multiple elements, stored in their registers. RMA
also extend register automata, by allowing arbitrary formulas, besides equality
predicates. We study the closure properties of RMA under union, concatenation,
Kleene+, complement and determinization and show that RMA, contrary to symbolic
automata, are not determinizable when viewed as recognizers, without taking the
output of transitions into account. However, when a window operator, a
quintessential feature in Complex Event Processing, is used, RMA are indeed
determinizable even when viewed as recognizers. We present detailed algorithms
for constructing deterministic RMA from regular expressions extended with
-ary constraints. We show how RMA can be used in Complex Event Processing in
order to detect patterns upon streams of events, using a framework that
provides denotational and compositional semantics, and that allows for a
systematic treatment of such automata
The Isomorphism Problem for omega-Automatic Trees
The main result of this paper is that the isomorphism for omega-automatic
trees of finite height is at least has hard as second-order arithmetic and
therefore not analytical. This strengthens a recent result by Hjorth,
Khoussainov, Montalban, and Nies showing that the isomorphism problem for
omega-automatic structures is not . Moreover, assuming the
continuum hypothesis CH, we can show that the isomorphism problem for
omega-automatic trees of finite height is recursively equivalent with
second-order arithmetic. On the way to our main results, we show lower and
upper bounds for the isomorphism problem for omega-automatic trees of every
finite height: (i) It is decidable (-complete, resp,) for height 1 (2,
resp.), (ii) -hard and in for height 3, and (iii)
- and -hard and in (assuming CH)
for all n > 3. All proofs are elementary and do not rely on theorems from set
theory
A Framework to Handle Linear Temporal Properties in (\omega-)Regular Model Checking
Since the topic emerged several years ago, work on regular model checking has
mostly been devoted to the verification of state reachability and safety
properties. Though it was known that linear temporal properties could also be
checked within this framework, little has been done about working out the
corresponding details. This paper addresses this issue in the context of
regular model checking based on the encoding of states by finite or infinite
words. It works out the exact constructions to be used in both cases, and
proposes a partial solution to the problem resulting from the fact that
infinite computations of unbounded configurations might never contain the same
configuration twice, thus making cycle detection problematic
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
Model Learning: A Survey on Foundation, Tools and Applications
The quality and correct functioning of software components embedded in
electronic systems are of utmost concern especially for safety and
mission-critical systems. Model-based testing and formal verification
techniques can be employed to enhance the reliability of software systems.
Formal models form the basis and are prerequisite for the application of these
techniques. An emerging and promising model learning technique can complement
testing and verification techniques by providing learned models of black box
systems fully automatically. This paper surveys one such state of the art
technique called model learning which recently has attracted much attention of
researchers especially from the domains of testing and verification. This
survey paper reviews and provides comparison summaries highlighting the merits
and shortcomings of learning techniques, algorithms, and tools which form the
basis of model learning. This paper also surveys the successful applications of
model learning technique in multidisciplinary fields making it promising for
testing and verification of realistic systems.Comment: 43 page
On (Omega-)Regular Model Checking
Checking infinite-state systems is frequently done by encoding infinite sets
of states as regular languages. Computing such a regular representation of,
say, the set of reachable states of a system requires acceleration techniques
that can finitely compute the effect of an unbounded number of transitions.
Among the acceleration techniques that have been proposed, one finds both
specific and generic techniques. Specific techniques exploit the particular
type of system being analyzed, e.g. a system manipulating queues or integers,
whereas generic techniques only assume that the transition relation is
represented by a finite-state transducer, which has to be iterated. In this
paper, we investigate the possibility of using generic techniques in cases
where only specific techniques have been exploited so far. Finding that
existing generic techniques are often not applicable in cases easily handled by
specific techniques, we have developed a new approach to iterating transducers.
This new approach builds on earlier work, but exploits a number of new
conceptual and algorithmic ideas, often induced with the help of experiments,
that give it a broad scope, as well as good performances
An Effective Decision Procedure for Linear Arithmetic with Integer and Real Variables
This paper considers finite-automata based algorithms for handling linear
arithmetic with both real and integer variables. Previous work has shown that
this theory can be dealt with by using finite automata on infinite words, but
this involves some difficult and delicate to implement algorithms. The
contribution of this paper is to show, using topological arguments, that only a
restricted class of automata on infinite words are necessary for handling real
and integer linear arithmetic. This allows the use of substantially simpler
algorithms, which have been successfully implemented.Comment: 20 pages, 6 figure
Logic Column 19: Symbolic Model Checking for Temporal-Epistemic Logics
This article surveys some of the recent work in verification of temporal
epistemic logic via symbolic model checking, focusing on OBDD-based and
SAT-based approaches for epistemic logics built on discrete and real-time
branching time temporal logics.Comment: 23 page
Quadratic Word Equations with Length Constraints, Counter Systems, and Presburger Arithmetic with Divisibility
Word equations are a crucial element in the theoretical foundation of
constraint solving over strings, which have received a lot of attention in
recent years. A word equation relates two words over string variables and
constants. Its solution amounts to a function mapping variables to constant
strings that equate the left and right hand sides of the equation. While the
problem of solving word equations is decidable, the decidability of the problem
of solving a word equation with a length constraint (i.e., a constraint
relating the lengths of words in the word equation) has remained a
long-standing open problem. In this paper, we focus on the subclass of
quadratic word equations, i.e., in which each variable occurs at most twice. We
first show that the length abstractions of solutions to quadratic word
equations are in general not Presburger-definable. We then describe a class of
counter systems with Presburger transition relations which capture the length
abstraction of a quadratic word equation with regular constraints. We provide
an encoding of the effect of a simple loop of the counter systems in the theory
of existential Presburger Arithmetic with divisibility (PAD). Since PAD is
decidable, we get a decision procedure for quadratic words equations with
length constraints for which the associated counter system is \emph{flat}
(i.e., all nodes belong to at most one cycle). We show a decidability result
(in fact, also an NP algorithm with a PAD oracle) for a recently proposed
NP-complete fragment of word equations called regular-oriented word equations,
together with length constraints. Decidability holds when the constraints are
additionally extended with regular constraints with a 1-weak control structure.Comment: 18 page
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