2,360 research outputs found
Revisiting Interactive Markov Chains
Abstract The usage of process algebras for the performance modeling and evaluation of concurrent systems turned out to be convenient due to their feature of compositionality. A particularly simple and elegant solution in this field is the calculus of Interactive Markov Chains (IMCs), where the behavior of processes is just represented by Continuous Time Markov Chains extended with action transitions representing process interaction. The main advantage of IMCs with respect to other existing approaches is that a notion of bisimulation which abstracts from Ï„-transitions ("complete" interactions) can be defined which is a congruence. However in the original definition of the calculus of IMCs the high potentiality of compositionally minimizing the system state space given by the usage of a "weak" notion of equivalence and the elegance of the approach is somehow limited by the fact that the equivalence adopted over action transitions is a finer variant of Milner's observational congruence that distinguishes Ï„-divergent "Zeno" processes from non-divergent ones. In this paper we show that it is possible to reformulate the calculus of IMCs in such a way that we can just rely on simple standard observational congruence. Moreover we show that the new calculus is the first Markovian process algebra allowing for a new notion of Markovian bisimulation equivalence which is coarser than the standard one
Markovian Testing Equivalence and Exponentially Timed Internal Actions
In the theory of testing for Markovian processes developed so far,
exponentially timed internal actions are not admitted within processes. When
present, these actions cannot be abstracted away, because their execution takes
a nonzero amount of time and hence can be observed. On the other hand, they
must be carefully taken into account, in order not to equate processes that are
distinguishable from a timing viewpoint. In this paper, we recast the
definition of Markovian testing equivalence in the framework of a Markovian
process calculus including exponentially timed internal actions. Then, we show
that the resulting behavioral equivalence is a congruence, has a sound and
complete axiomatization, has a modal logic characterization, and can be decided
in polynomial time
Weak Markovian Bisimulation Congruences and Exact CTMC-Level Aggregations for Concurrent Processes
We have recently defined a weak Markovian bisimulation equivalence in an
integrated-time setting, which reduces sequences of exponentially timed
internal actions to individual exponentially timed internal actions having the
same average duration and execution probability as the corresponding sequences.
This weak Markovian bisimulation equivalence is a congruence for sequential
processes with abstraction and turns out to induce an exact CTMC-level
aggregation at steady state for all the considered processes. However, it is
not a congruence with respect to parallel composition. In this paper, we show
how to generalize the equivalence in a way that a reasonable tradeoff among
abstraction, compositionality, and exactness is achieved for concurrent
processes. We will see that, by enhancing the abstraction capability in the
presence of concurrent computations, it is possible to retrieve the congruence
property with respect to parallel composition, with the resulting CTMC-level
aggregation being exact at steady state only for a certain subset of the
considered processes.Comment: In Proceedings QAPL 2012, arXiv:1207.055
Prediction and Power in Molecular Sensors: Uncertainty and Dissipation When Conditionally Markovian Channels Are Driven by Semi-Markov Environments
Sensors often serve at least two purposes: predicting their input and
minimizing dissipated heat. However, determining whether or not a particular
sensor is evolved or designed to be accurate and efficient is difficult. This
arises partly from the functional constraints being at cross purposes and
partly since quantifying the predictive performance of even in silico sensors
can require prohibitively long simulations. To circumvent these difficulties,
we develop expressions for the predictive accuracy and thermodynamic costs of
the broad class of conditionally Markovian sensors subject to unifilar hidden
semi-Markov (memoryful) environmental inputs. Predictive metrics include the
instantaneous memory and the mutual information between present sensor state
and input future, while dissipative metrics include power consumption and the
nonpredictive information rate. Success in deriving these formulae relies
heavily on identifying the environment's causal states, the input's minimal
sufficient statistics for prediction. Using these formulae, we study the
simplest nontrivial biological sensor model---that of a Hill molecule,
characterized by the number of ligands that bind simultaneously, the sensor's
cooperativity. When energetic rewards are proportional to total predictable
information, the closest cooperativity that optimizes the total energy budget
generally depends on the environment's past hysteretically. In this way, the
sensor gains robustness to environmental fluctuations. Given the simplicity of
the Hill molecule, such hysteresis will likely be found in more complex
predictive sensors as well. That is, adaptations that only locally optimize
biochemical parameters for prediction and dissipation can lead to sensors that
"remember" the past environment.Comment: 21 pages, 4 figures,
http://csc.ucdavis.edu/~cmg/compmech/pubs/piness.ht
- …