63 research outputs found
On Termination for Faulty Channel Machines
A channel machine consists of a finite controller together with several fifo
channels; the controller can read messages from the head of a channel and write
messages to the tail of a channel. In this paper, we focus on channel machines
with insertion errors, i.e., machines in whose channels messages can
spontaneously appear. Such devices have been previously introduced in the study
of Metric Temporal Logic. We consider the termination problem: are all the
computations of a given insertion channel machine finite? We show that this
problem has non-elementary, yet primitive recursive complexity
On computing fixpoints in well-structured regular model checking, with applications to lossy channel systems
We prove a general finite convergence theorem for "upward-guarded" fixpoint
expressions over a well-quasi-ordered set. This has immediate applications in
regular model checking of well-structured systems, where a main issue is the
eventual convergence of fixpoint computations. In particular, we are able to
directly obtain several new decidability results on lossy channel systems.Comment: 16 page
Maximal decidable fragments of Halpern and Shoham's modal logic of intervals
In this paper, we focus our attention on the fragment of
Halpern and Shoham's modal logic of intervals (HS) that
features four modal operators corresponding to the
relations ``meets'', ``met by'', ``begun by'', and
``begins'' of Allen's interval algebra (AAbarBBbar logic).
AAbarBBbar properly extends interesting interval temporal
logics recently investigated in the literature, such as the
logic BBbar of Allen's ``begun by/begins'' relations and
propositional neighborhood logic AAbar, in its many
variants (including metric ones). We prove that the satisfiability
problem for AAbarBBbar, interpreted over finite linear orders,
is decidable, but not primitive recursive (as a matter of fact,
AAbarBBbar turns out to be maximal with respect to decidability). Then, we show that it becomes undecidable when AAbarBBbar is interpreted over classes of linear orders that contains at least one linear order with an infinitely ascending sequence, thus including the natural time flows N, Z, Q, and R
Verifying Recursive Active Documents with Positive Data Tree Rewriting
This paper proposes a data tree-rewriting framework for modeling evolving
documents. The framework is close to Guarded Active XML, a platform used for
handling XML repositories evolving through web services. We focus on automatic
verification of properties of evolving documents that can contain data from an
infinite domain. We establish the boundaries of decidability, and show that
verification of a {\em positive} fragment that can handle recursive service
calls is decidable. We also consider bounded model-checking in our data
tree-rewriting framework and show that it is \nexptime-complete
The decision problem of modal product logics with a diagonal, and faulty counter machines
In the propositional modal (and algebraic) treatment of two-variable
first-order logic equality is modelled by a `diagonal' constant, interpreted in
square products of universal frames as the identity (also known as the
`diagonal') relation. Here we study the decision problem of products of two
arbitrary modal logics equipped with such a diagonal. As the presence or
absence of equality in two-variable first-order logic does not influence the
complexity of its satisfiability problem, one might expect that adding a
diagonal to product logics in general is similarly harmless. We show that this
is far from being the case, and there can be quite a big jump in complexity,
even from decidable to the highly undecidable. Our undecidable logics can also
be viewed as new fragments of first- order logic where adding equality changes
a decidable fragment to undecidable. We prove our results by a novel
application of counter machine problems. While our formalism apparently cannot
force reliable counter machine computations directly, the presence of a unique
diagonal in the models makes it possible to encode both lossy and
insertion-error computations, for the same sequence of instructions. We show
that, given such a pair of faulty computations, it is then possible to
reconstruct a reliable run from them
Regular Model Checking Using Inference of Regular Languages
Regular model checking is a method for verifying infinite-state systems based on coding their configurations as words over a finite alphabet, sets of configurations as finite automata, and transitions as finite transducers. We introduce a new general approach to regular model checking based on inference of regular languages. The method builds upon the observation that for infinite-state systems whose behaviour can be modelled using length-preserving transducers, there is a finite computation for obtaining all reachable configurations up to a certain length n. These configurations are a (positive) sample of the reachable configurations of the given system, whereas all other words up to length n are a negative sample. Then, methods of inference of regular languages can be used to generalize the sample to the full reachability set (or an overapproximation of it). We have implemented our method in a prototype tool which shows that our approach is competitive on a number of concrete examples. Furthermore, in contrast to all other existing regular model checking methods, termination is guaranteed in general for all systems with regular sets of reachable configurations. The method can be applied in a similar way to dealing with reachability relations instead of reachability sets too
Parameterized Verification of Algorithms for Oblivious Robots on a Ring
We study verification problems for autonomous swarms of mobile robots that
self-organize and cooperate to solve global objectives. In particular, we focus
in this paper on the model proposed by Suzuki and Yamashita of anonymous robots
evolving in a discrete space with a finite number of locations (here, a ring).
A large number of algorithms have been proposed working for rings whose size is
not a priori fixed and can be hence considered as a parameter. Handmade
correctness proofs of these algorithms have been shown to be error-prone, and
recent attention had been given to the application of formal methods to
automatically prove those. Our work is the first to study the verification
problem of such algorithms in the parameter-ized case. We show that safety and
reachability problems are undecidable for robots evolving asynchronously. On
the positive side, we show that safety properties are decidable in the
synchronous case, as well as in the asynchronous case for a particular class of
algorithms. Several properties on the protocol can be decided as well. Decision
procedures rely on an encoding in Presburger arithmetics formulae that can be
verified by an SMT-solver. Feasibility of our approach is demonstrated by the
encoding of several case studies
Maximal decidable fragments of Halpern and Shoham's modal logic of intervals
In this paper, we focus our attention on the fragment of
Halpern and Shoham's modal logic of intervals (HS) that
features four modal operators corresponding to the
relations ``meets'', ``met by'', ``begun by'', and
``begins'' of Allen's interval algebra (AAbarBBbar logic).
AAbarBBbar properly extends interesting interval temporal
logics recently investigated in the literature, such as the
logic BBbar of Allen's ``begun by/begins'' relations and
propositional neighborhood logic AAbar, in its many
variants (including metric ones). We prove that the satisfiability
problem for AAbarBBbar, interpreted over finite linear orders,
is decidable, but not primitive recursive (as a matter of fact,
AAbarBBbar turns out to be maximal with respect to decidability). Then, we show that it becomes undecidable when AAbarBBbar is interpreted over classes of linear orders that contains at least one linear order with an infinitely ascending sequence, thus including the natural time flows N, Z, Q, and R
Place-Boundedness for Vector Addition Systems with one zero-test
Reachability and boundedness problems have been shown decidable for Vector Addition Systems with one zero-test. Surprisingly, place-boundedness remained open. We provide here a variation of the Karp-Miller algorithm to compute a basis of the downward closure of the reachability set which allows to decide place-boundedness. This forward algorithm is able to pass the zero-tests thanks to a finer cover, hybrid between the reachability and cover sets, reclaiming accuracy on one component. We show that this filtered cover is still recursive, but that equality of two such filtered covers, even for usual Vector Addition Systems (with no zero-test), is undecidable
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