On Deterministic Linearizable Set Agreement Objects

A recent work showed that, for all n and k, there is a linearizable (n,k)-set agreement object O_L that is equivalent to the (n,k)-set agreement task [David Yu Cheng Chan et al., 2017]: given O_L, it is possible to solve the (n,k)-set agreement task, and given any algorithm that solves the (n,k)-set agreement task (and registers), it is possible to implement O_L. This linearizable object O_L, however, is not deterministic. It turns out that there is also a deterministic (n,k)-set agreement object O_D that is equivalent to the (n,k)-set agreement task, but this deterministic object O_D is not linearizable. This raises the question whether there exists a deterministic and linearizable (n,k)-set agreement object that is equivalent to the (n,k)-set agreement task. Here we show that in general the answer is no: specifically, we prove that for all n ? 4, every deterministic linearizable (n,2)-set agreement object is strictly stronger than the (n,2)-set agreement task. We prove this by showing that, for all n ? 4, every deterministic and linearizable (n,2)-set agreement object (together with registers) can be used to solve 2-consensus, whereas it is known that the (n,2)-set agreement task cannot do so. For a natural subset of (n,2)-set agreement objects, we prove that this result holds even for n = 3

Computing with cells: membrane systems - some complexity issues.

Membrane computing is a branch of natural computing which abstracts computing models from the structure and the functioning of the living cell. The main ingredients of membrane systems, called P systems, are (i) the membrane structure, which consists of a hierarchical arrangements of membranes which delimit compartments where (ii) multisets of symbols, called objects, evolve according to (iii) sets of rules which are localised and associated with compartments. By using the rules in a nondeterministic/deterministic maximally parallel manner, transitions between the system configurations can be obtained. A sequence of transitions is a computation of how the system is evolving. Various ways of controlling the transfer of objects from one membrane to another and applying the rules, as well as possibilities to dissolve, divide or create membranes have been studied. Membrane systems have a great potential for implementing massively concurrent systems in an efficient way that would allow us to solve currently intractable problems once future biotechnology gives way to a practical bio-realization. In this paper we survey some interesting and fundamental complexity issues such as universality vs. nonuniversality, determinism vs. nondeterminism, membrane and alphabet size hierarchies, characterizations of context-sensitive languages and other language classes and various notions of parallelism

Divided we stand: Parallel distributed stack memory management

We present an overview of the stack-based memory management techniques that we used in our non-deterministic and-parallel Prolog systems: &-Prolog and DASWAM. We believe that the problems associated with non-deterministic and-parallel systems are more general than those encountered in or-parallel and deterministic and-parallel systems, which can be seen as subsets of this more general case. We develop on the previously proposed "marker scheme", lifting some of the restrictions associated with the selection of goals while keeping (virtual) memory consumption down. We also review some of the other problems associated with the stack-based management scheme, such as handling of forward and backward execution, cut, and roll-backs

Static Analysis of Deterministic Negotiations

Negotiation diagrams are a model of concurrent computation akin to workflow Petri nets. Deterministic negotiation diagrams, equivalent to the much studied and used free-choice workflow Petri nets, are surprisingly amenable to verification. Soundness (a property close to deadlock-freedom) can be decided in PTIME. Further, other fundamental questions like computing summaries or the expected cost, can also be solved in PTIME for sound deterministic negotiation diagrams, while they are PSPACE-complete in the general case. In this paper we generalize and explain these results. We extend the classical "meet-over-all-paths" (MOP) formulation of static analysis problems to our concurrent setting, and introduce Mazurkiewicz-invariant analysis problems, which encompass the questions above and new ones. We show that any Mazurkiewicz-invariant analysis problem can be solved in PTIME for sound deterministic negotiations whenever it is in PTIME for sequential flow-graphs---even though the flow-graph of a deterministic negotiation diagram can be exponentially larger than the diagram itself. This gives a common explanation to the low-complexity of all the analysis questions studied so far. Finally, we show that classical gen/kill analyses are also an instance of our framework, and obtain a PTIME algorithm for detecting anti-patterns in free-choice workflow Petri nets. Our result is based on a novel decomposition theorem, of independent interest, showing that sound deterministic negotiation diagrams can be hierarchically decomposed into (possibly overlapping) smaller sound diagrams.Comment: To appear in the Proceedings of LICS 2017, IEEE Computer Societ

Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems

Approximate Bayesian computation methods can be used to evaluate posterior distributions without having to calculate likelihoods. In this paper we discuss and apply an approximate Bayesian computation (ABC) method based on sequential Monte Carlo (SMC) to estimate parameters of dynamical models. We show that ABC SMC gives information about the inferability of parameters and model sensitivity to changes in parameters, and tends to perform better than other ABC approaches. The algorithm is applied to several well known biological systems, for which parameters and their credible intervals are inferred. Moreover, we develop ABC SMC as a tool for model selection; given a range of different mathematical descriptions, ABC SMC is able to choose the best model using the standard Bayesian model selection apparatus.Comment: 26 pages, 9 figure

A Modular Formalization of Reversibility for Concurrent Models and Languages

Causal-consistent reversibility is the reference notion of reversibility for concurrency. We introduce a modular framework for defining causal-consistent reversible extensions of concurrent models and languages. We show how our framework can be used to define reversible extensions of formalisms as different as CCS and concurrent X-machines. The generality of the approach allows for the reuse of theories and techniques in different settings.Comment: In Proceedings ICE 2016, arXiv:1608.0313

Synchronous and Asynchronous Recursive Random Scale-Free Nets

We investigate the differences between scale-free recursive nets constructed by a synchronous, deterministic updating rule (e.g., Apollonian nets), versus an asynchronous, random sequential updating rule (e.g., random Apollonian nets). We show that the dramatic discrepancies observed recently for the degree exponent in these two cases result from a biased choice of the units to be updated sequentially in the asynchronous version

Tree transducers, L systems, and two-way machines

A relationship between parallel rewriting systems and two-way machines is investigated. Restrictions on the “copying power” of these devices endow them with rich structuring and give insight into the issues of determinism, parallelism, and copying. Among the parallel rewriting systems considered are the top-down tree transducer; the generalized syntax-directed translation scheme and the ETOL system, and among the two-way machines are the tree-walking automaton, the two-way finite-state transducer, and (generalizations of) the one-way checking stack automaton. The. relationship of these devices to macro grammars is also considered. An effort is made .to provide a systematic survey of a number of existing results