3,169 research outputs found
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
Performance evaluation of an emergency call center: tropical polynomial systems applied to timed Petri nets
We analyze a timed Petri net model of an emergency call center which
processes calls with different levels of priority. The counter variables of the
Petri net represent the cumulated number of events as a function of time. We
show that these variables are determined by a piecewise linear dynamical
system. We also prove that computing the stationary regimes of the associated
fluid dynamics reduces to solving a polynomial system over a tropical
(min-plus) semifield of germs. This leads to explicit formul{\ae} expressing
the throughput of the fluid system as a piecewise linear function of the
resources, revealing the existence of different congestion phases. Numerical
experiments show that the analysis of the fluid dynamics yields a good
approximation of the real throughput.Comment: 21 pages, 4 figures. A shorter version can be found in the
proceedings of the conference FORMATS 201
High clarity speech separation using synchro extracting transform
Degenerate unmixing estimation technique (DUET) is the most ideal blind source separation (BSS) method for underdetermined conditions with number of sources exceeds number of mixtures. Estimation of mixing parameters which is the most critical step in the DUET algorithm, is developed based on the characteristic feature of sparseness of speech signals in time frequency (TF) domain. Hence, DUET relies on the clarity of time frequency representation (TFR) and even the slightest interference in the TF plane will be detrimental to the unmixing performance. In conventional DUET algorithm, short time Fourier transform (STFT) is utilized for extracting the TFR of speech signals. However, STFT can provide on limited sharpness to the TFR due to its inherent conceptual limitations, which worsens under noise contamination. This paper presents the application of post-processing techniques like synchro squeezed transform (SST) and synchro extracting transform (SET) to the DUET algorithm, to improve the TF resolution. The performance enhancement is evaluated both qualitatively and quantitatively by visual inspection, Renyi entropy of TFR and objective measures of speech signals. The results show enhancement in TF resolution and high clarity signal reconstruction. The method also provides adequate robustness to noise contamination
Zero-Reachability in Probabilistic Multi-Counter Automata
We study the qualitative and quantitative zero-reachability problem in
probabilistic multi-counter systems. We identify the undecidable variants of
the problems, and then we concentrate on the remaining two cases. In the first
case, when we are interested in the probability of all runs that visit zero in
some counter, we show that the qualitative zero-reachability is decidable in
time which is polynomial in the size of a given pMC and doubly exponential in
the number of counters. Further, we show that the probability of all
zero-reaching runs can be effectively approximated up to an arbitrarily small
given error epsilon > 0 in time which is polynomial in log(epsilon),
exponential in the size of a given pMC, and doubly exponential in the number of
counters. In the second case, we are interested in the probability of all runs
that visit zero in some counter different from the last counter. Here we show
that the qualitative zero-reachability is decidable and SquareRootSum-hard, and
the probability of all zero-reaching runs can be effectively approximated up to
an arbitrarily small given error epsilon > 0 (these result applies to pMC
satisfying a suitable technical condition that can be verified in polynomial
time). The proof techniques invented in the second case allow to construct
counterexamples for some classical results about ergodicity in stochastic Petri
nets.Comment: 20 page
Algorithmic Verification of Asynchronous Programs
Asynchronous programming is a ubiquitous systems programming idiom to manage
concurrent interactions with the environment. In this style, instead of waiting
for time-consuming operations to complete, the programmer makes a non-blocking
call to the operation and posts a callback task to a task buffer that is
executed later when the time-consuming operation completes. A co-operative
scheduler mediates the interaction by picking and executing callback tasks from
the task buffer to completion (and these callbacks can post further callbacks
to be executed later). Writing correct asynchronous programs is hard because
the use of callbacks, while efficient, obscures program control flow.
We provide a formal model underlying asynchronous programs and study
verification problems for this model. We show that the safety verification
problem for finite-data asynchronous programs is expspace-complete. We show
that liveness verification for finite-data asynchronous programs is decidable
and polynomial-time equivalent to Petri Net reachability. Decidability is not
obvious, since even if the data is finite-state, asynchronous programs
constitute infinite-state transition systems: both the program stack and the
task buffer of pending asynchronous calls can be potentially unbounded.
Our main technical construction is a polynomial-time semantics-preserving
reduction from asynchronous programs to Petri Nets and conversely. The
reduction allows the use of algorithmic techniques on Petri Nets to the
verification of asynchronous programs.
We also study several extensions to the basic models of asynchronous programs
that are inspired by additional capabilities provided by implementations of
asynchronous libraries, and classify the decidability and undecidability of
verification questions on these extensions.Comment: 46 pages, 9 figure
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
Locality and Singularity for Store-Atomic Memory Models
Robustness is a correctness notion for concurrent programs running under
relaxed consistency models. The task is to check that the relaxed behavior
coincides (up to traces) with sequential consistency (SC). Although
computationally simple on paper (robustness has been shown to be
PSPACE-complete for TSO, PGAS, and Power), building a practical robustness
checker remains a challenge. The problem is that the various relaxations lead
to a dramatic number of computations, only few of which violate robustness.
In the present paper, we set out to reduce the search space for robustness
checkers. We focus on store-atomic consistency models and establish two
completeness results. The first result, called locality, states that a
non-robust program always contains a violating computation where only one
thread delays commands. The second result, called singularity, is even stronger
but restricted to programs without lightweight fences. It states that there is
a violating computation where a single store is delayed.
As an application of the results, we derive a linear-size source-to-source
translation of robustness to SC-reachability. It applies to general programs,
regardless of the data domain and potentially with an unbounded number of
threads and with unbounded buffers. We have implemented the translation and
verified, for the first time, PGAS algorithms in a fully automated fashion. For
TSO, our analysis outperforms existing tools
The Parametric Ordinal-Recursive Complexity of Post Embedding Problems
Post Embedding Problems are a family of decision problems based on the
interaction of a rational relation with the subword embedding ordering, and are
used in the literature to prove non multiply-recursive complexity lower bounds.
We refine the construction of Chambart and Schnoebelen (LICS 2008) and prove
parametric lower bounds depending on the size of the alphabet.Comment: 16 + vii page
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