1,554 research outputs found
Reachability for Two-Counter Machines with One Test and One Reset
We prove that the reachability relation of two-counter machines with one zero-test and one reset is Presburger-definable and effectively computable. Our proof is based on the introduction of two classes of Presburger-definable relations effectively stable by transitive closure. This approach generalizes and simplifies the existing different proofs and it solves an open problem introduced by Finkel and Sutre in 2000
Dense-choice Counter Machines revisited
This paper clarifies the picture about Dense-choice Counter Machines, which
have been less studied than (discrete) Counter Machines. We revisit the
definition of "Dense Counter Machines" so that it now extends (discrete)
Counter Machines, and we provide new undecidability and decidability results.
Using the first-order additive mixed theory of reals and integers, we give a
logical characterization of the sets of configurations reachable by
reversal-bounded Dense-choice Counter Machines
Forward Analysis and Model Checking for Trace Bounded WSTS
We investigate a subclass of well-structured transition systems (WSTS), the
bounded---in the sense of Ginsburg and Spanier (Trans. AMS 1964)---complete
deterministic ones, which we claim provide an adequate basis for the study of
forward analyses as developed by Finkel and Goubault-Larrecq (Logic. Meth.
Comput. Sci. 2012). Indeed, we prove that, unlike other conditions considered
previously for the termination of forward analysis, boundedness is decidable.
Boundedness turns out to be a valuable restriction for WSTS verification, as we
show that it further allows to decide all -regular properties on the
set of infinite traces of the system
The Reachability Problem for Petri Nets is Not Elementary
Petri nets, also known as vector addition systems, are a long established
model of concurrency with extensive applications in modelling and analysis of
hardware, software and database systems, as well as chemical, biological and
business processes. The central algorithmic problem for Petri nets is
reachability: whether from the given initial configuration there exists a
sequence of valid execution steps that reaches the given final configuration.
The complexity of the problem has remained unsettled since the 1960s, and it is
one of the most prominent open questions in the theory of verification.
Decidability was proved by Mayr in his seminal STOC 1981 work, and the
currently best published upper bound is non-primitive recursive Ackermannian of
Leroux and Schmitz from LICS 2019. We establish a non-elementary lower bound,
i.e. that the reachability problem needs a tower of exponentials of time and
space. Until this work, the best lower bound has been exponential space, due to
Lipton in 1976. The new lower bound is a major breakthrough for several
reasons. Firstly, it shows that the reachability problem is much harder than
the coverability (i.e., state reachability) problem, which is also ubiquitous
but has been known to be complete for exponential space since the late 1970s.
Secondly, it implies that a plethora of problems from formal languages, logic,
concurrent systems, process calculi and other areas, that are known to admit
reductions from the Petri nets reachability problem, are also not elementary.
Thirdly, it makes obsolete the currently best lower bounds for the reachability
problems for two key extensions of Petri nets: with branching and with a
pushdown stack.Comment: Final version of STOC'1
History-Register Automata
Programs with dynamic allocation are able to create and use an unbounded
number of fresh resources, such as references, objects, files, etc. We propose
History-Register Automata (HRA), a new automata-theoretic formalism for
modelling such programs. HRAs extend the expressiveness of previous approaches
and bring us to the limits of decidability for reachability checks. The
distinctive feature of our machines is their use of unbounded memory sets
(histories) where input symbols can be selectively stored and compared with
symbols to follow. In addition, stored symbols can be consumed or deleted by
reset. We show that the combination of consumption and reset capabilities
renders the automata powerful enough to imitate counter machines, and yields
closure under all regular operations apart from complementation. We moreover
examine weaker notions of HRAs which strike different balances between
expressiveness and effectiveness.Comment: LMCS (improved version of FoSSaCS
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
Revisiting Synthesis for One-Counter Automata
We study the (parameter) synthesis problem for one-counter automata with
parameters. One-counter automata are obtained by extending classical
finite-state automata with a counter whose value can range over non-negative
integers and be tested for zero. The updates and tests applicable to the
counter can further be made parametric by introducing a set of integer-valued
variables called parameters. The synthesis problem for such automata asks
whether there exists a valuation of the parameters such that all infinite runs
of the automaton satisfy some omega-regular property. Lechner showed that (the
complement of) the problem can be encoded in a restricted one-alternation
fragment of Presburger arithmetic with divisibility. In this work (i) we argue
that said fragment, called AERPADPLUS, is unfortunately undecidable.
Nevertheless, by a careful re-encoding of the problem into a decidable
restriction of AERPADPLUS, (ii) we prove that the synthesis problem is
decidable in general and in N2EXP for several fixed omega-regular properties.
Finally, (iii) we give a polynomial-space algorithm for the special case of the
problem where parameters can only be used in tests, and not updates, of the
counter
Revisiting Reachability in Timed Automata
We revisit a fundamental result in real-time verification, namely that the
binary reachability relation between configurations of a given timed automaton
is definable in linear arithmetic over the integers and reals. In this paper we
give a new and simpler proof of this result, building on the well-known
reachability analysis of timed automata involving difference bound matrices.
Using this new proof, we give an exponential-space procedure for model checking
the reachability fragment of the logic parametric TCTL. Finally we show that
the latter problem is NEXPTIME-hard
Constraint-Based Heuristic On-line Test Generation from Non-deterministic I/O EFSMs
We are investigating on-line model-based test generation from
non-deterministic output-observable Input/Output Extended Finite State Machine
(I/O EFSM) models of Systems Under Test (SUTs). We propose a novel
constraint-based heuristic approach (Heuristic Reactive Planning Tester (xRPT))
for on-line conformance testing non-deterministic SUTs. An indicative feature
of xRPT is the capability of making reasonable decisions for achieving the test
goals in the on-line testing process by using the results of off-line bounded
static reachability analysis based on the SUT model and test goal
specification. We present xRPT in detail and make performance comparison with
other existing search strategies and approaches on examples with varying
complexity.Comment: In Proceedings MBT 2012, arXiv:1202.582
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