Target-oriented Petri Net Synthesis

When a Petri net is synthesised from a labelled transition system, it is frequently desirable that certain additional constraints are fulfilled. For example, in circuit design, one is often interested in constructing safe Petri nets. Targeting such subclasses of Petri nets is not necessarily computationally more efficient than targeting the whole class. For example, targeting safe nets is known to be NP-complete while targeting the full class of place/transition nets is polynomial, in the size of the transition system. In this paper, several classes of Petri nets are examined, and their suitability for being targeted through efficient synthesis from labelled transition systems is studied and assessed. The focus is on choice-free Petri nets and some of their subclasses. It is described how they can be synthesised efficiently from persistent transition systems, summarising and streamlining in tutorial style some of the authors’ and their groups’ work over the past few years.

L-systems from 3D-imaging of Phenotypes of Arborized Structures

Biology is 3D. Therefore, it is important to be able to analyze phenomena in a spatio-temporal manner. Different fields in computational sciences are useful for analysis in biology; i.e. image analysis, pattern recognition and machine learning. To fit an empirical model to a higher abstraction, however, theoretical computer science methods are probed. We explore the construction of empirical 3D graphical models and develop abstractions from these models in L-systems. These systems are provided with a profound formalization in a grammar allowing generalization and exploration of mathematical structures in topologies. The connections between these computational approaches are illustrated by a case study of the development of the lactiferous duct in mice and the phenotypical effects from different environmental conditions we can observe on it. We have constructed a workflow to get 3D models from different experimental conditions and use these models to extract features. Our aim is to construct an abstraction of these 3D models to an L-system from features that we have measured. From our measurements we can make the productions for an L-system. In this manner we can formalize the arborization of the lactiferous duct under different environmental conditions and capture different observations. All considered, this paper illustrates the joint of empirical with theoretical computational sciences and the augmentation of the interpretation of the results. At the same time, it shows a method to analyze complex 3D topologies and produces archetypes for developmental configurations.

Network Controllability Analysis of Three Multiple-myeloma Patient Genetic Mutation Datasets

Network controllability focuses on the concept of driving the dynamical system associated to a directed network of interactions from an arbitrary initial state to an arbitrary final state, through a well-chosen set of input functions applied in a minimal number of so-called input nodes. In earlier studies we and other groups demonstrated the potential of applying this concept in medicine. A directed network of interactions may be built around the main known drivers of the disease being studied, and then analysed to identify combinations of drug targets controlling survivability-essential genes in the network. This paper takes the next step and focuses on patient data. We demonstrate that comprehensive protein-protein interaction networks can be built around patient genetic data, and that network controllability can be used to identify possible personalised drug combinations. We discuss the algorithmic methods that can be used to construct and analyse these networks.

Algebraic Structure of Step Traces and Interval Traces

Traces and their extensions as comtraces, step traces and interval traces are quotient monoids over sequences or step sequences that play an important role in the formal analysis and verification of concurrent systems. Step traces are generalizations of comtraces and classical traces while interval traces are specialized traces that can deal with interval order semantics. The algebraic structures and their properties as projections, hidings, canonical forms and other invariants are very well established for traces and fairly well established for comtraces. For step traces and interval traces they are the main subject of this paper.

On Shuffling a Word with its Letter-to-Letter Substitution

Denote by ⧢ the operation of interleaving, or shuffling, of words. We prove that, given a regular language R and a letter-to-letter morphism ϕ, it is undecidable whether or not there exists a word w such that w ⧢ ϕ(w) ∩ R ≠ ∅.

Roots and Powers in Regular Languages: Recognizing Nonregular Properties by Finite Automata

It is well known that the set of powers of any given order, for example squares, in a regular language need not be regular. Nevertheless, finite automata can identify them via their roots. More precisely, we recall that, given a regular language L, the set of square roots of L is regular. The same holds true for the nth roots for any n and for the set of all nontrivial roots; we give a concrete construction for all of them. Using the above result, we obtain decision algorithms for many natural problems on powers. For example, it is decidable, given two regular languages, whether they contain the same number of squares at each length. Finally, we give an exponential lower bound on the size of automata identifying powers in regular languages. Moreover, we highlight interesting behavior differences between taking fractional powers of regular languages and taking prefixes of a fractional length. Indeed, fractional roots in a regular language can typically not be identified by finite automata.

Dynamic Exploration of Multi-agent Systems with Periodic Timed Tasks

We formalise and study multi-agent timed models MAPTs (Multi-Agent with Periodic timed Tasks), where each agent is associated with a regular timed schema upon which all possible actions of the agent rely. MAPTs allow for an accelerated semantics and a layered structure of the state space, so that it is possible to explore the latter dynamically and use heuristics to greatly reduce the computation time needed to address reachability problems. We use an available tool for the Petri net implementation of MAPTs, to explore the state space of autonomous vehicle systems. Then, we compare this exploration with timed automata-based approaches in terms of expressiveness of available queries and computation time.

Comparing Degenerate Strings

Uncertain sequences are compact representations of sets of similar strings. They highlight common segments by collapsing them, and explicitly represent varying segments by listing all possible options. A generalized degenerate string (GD string) is a type of uncertain sequence. Formally, a GD string Ŝ is a sequence of n sets of strings of total size N, where the ith set contains strings of the same length ki but this length can vary between different sets. We denote by W the sum of these lengths k0, k1, …, kn-1. Our main result is an O(N + M)-time algorithm for deciding whether two GD strings of total sizes N and M, respectively, over an integer alphabet, have a non-empty intersection. This result is based on a combinatorial result of independent interest: although the intersection of two GD strings can be exponential in the total size of the two strings, it can be represented in linear space. We then apply our string comparison tool to devise a simple algorithm for computing all palindromes in Ŝ in O(min{W, n2}N)-time. We complement this upper bound by showing a similar conditional lower bound for computing maximal palindromes in Ŝ. We also show that a result, which is essentially the same as our string comparison linear-time algorithm, can be obtained by employing an automata-based approach.

A Theory of Distributed Markov Chains

We present the theory of distributed Markov chains (DMCs). A DMC consists of a collection of communicating probabilistic agents in which the synchronizations determine the probability distribution for the next moves of the participating agents. The key feature of a DMC is that the synchronizations are deterministic, in the sense that any two simultaneously enabled synchronizations involve disjoint sets of agents. Using our theory of DMCs we show how one can analyze the behavior using the interleaved semantics of the model. A key point is, the transition system which defines the interleaved semantics is—except in degenerate cases—not a Markov chain. Hence one must develop new techniques to analyze these behaviors exhibiting both concurrency and stochasticity. After establishing the core theory we develop a statistical model checking procedure which verifies the dynamical properties of the trajectories generated by the the model. The specifications consist of Boolean combinations of component-wise bounded linear time temporal logic formulas. We also provide a probabilistic Petri net representation of DMCs and use it to derive a probabilistic event structure semantics.

Companions and an Essential Motion of a Reaction System

For a family of sets we consider elements that belong to the same sets within the family as companions. The global dynamics of a reactions system (as introduced by Ehrenfeucht and Rozenberg) can be represented by a directed graph, called a transition graph, which is uniquely determined by a one-out subgraph, called the 0-context graph. We consider the companion classes of the outsets of a transition graph and introduce a directed multigraph, called an essential motion, whose vertices are such companion classes. We show that all one-out graphs obtained from an essential motion represent 0-context graphs of reactions systems with isomorphic transition graphs. All such 0-context graphs are obtained from one another by swapping the outgoing edges of companion vertices.