Computational Complexity of Synchronization under Regular Commutative Constraints

Here we study the computational complexity of the constrained synchronization problem for the class of regular commutative constraint languages. Utilizing a vector representation of regular commutative constraint languages, we give a full classification of the computational complexity of the constraint synchronization problem. Depending on the constraint language, our problem becomes PSPACE-complete, NP-complete or polynomial time solvable. In addition, we derive a polynomial time decision procedure for the complexity of the constraint synchronization problem, given some constraint automaton accepting a commutative language as input.Comment: Published in COCOON 2020 (The 26th International Computing and Combinatorics Conference); 2nd version is update of the published version and 1st version; both contain a minor error, the assumption of maximality in the NP-c and PSPACE-c results (propositions 5 & 6) is missing, and of incomparability of the vectors in main theorem; fixed in this version. See (new) discussion after main theore

Minimally Constrained Stable Switched Systems and Application to Co-simulation

We propose an algorithm to restrict the switching signals of a constrained switched system in order to guarantee its stability, while at the same time attempting to keep the largest possible set of allowed switching signals. Our work is motivated by applications to (co-)simulation, where numerical stability is a hard constraint, but should be attained by restricting as little as possible the allowed behaviours of the simulators. We apply our results to certify the stability of an adaptive co-simulation orchestration algorithm, which selects the optimal switching signal at run-time, as a function of (varying) performance and accuracy requirements.Comment: Technical report complementing the following conference publication: Gomes, Cl\'audio, Beno\^it Legat, Rapha\"el Jungers, and Hans Vangheluwe. "Minimally Constrained Stable Switched Systems and Application to Co-Simulation." In IEEE Conference on Decision and Control. Miami Beach, FL, USA, 201

Weak Alternating Timed Automata

Alternating timed automata on infinite words are considered. The main result is a characterization of acceptance conditions for which the emptiness problem for these automata is decidable. This result implies new decidability results for fragments of timed temporal logics. It is also shown that, unlike for MITL, the characterisation remains the same even if no punctual constraints are allowed

The finite tiling problem is undecidable in the hyperbolic plane

In this paper, we consider the finite tiling problem which was proved undecidable in the Euclidean plane by Jarkko Kari in 1994. Here, we prove that the same problem for the hyperbolic plane is also undecidable

Building Responsive Systems from Physically-correct Specifications

Predictability - the ability to foretell that an implementation will not violate a set of specified reliability and timeliness requirements - is a crucial, highly desirable property of responsive embedded systems. This paper overviews a development methodology for responsive systems, which enhances predictability by eliminating potential hazards resulting from physically-unsound specifications. The backbone of our methodology is the Time-constrained Reactive Automaton (TRA) formalism, which adopts a fundamental notion of space and time that restricts expressiveness in a way that allows the specification of only reactive, spontaneous, and causal computation. Using the TRA model, unrealistic systems - possessing properties such as clairvoyance, caprice, in finite capacity, or perfect timing - cannot even be specified. We argue that this "ounce of prevention" at the specification level is likely to spare a lot of time and energy in the development cycle of responsive systems - not to mention the elimination of potential hazards that would have gone, otherwise, unnoticed. The TRA model is presented to system developers through the CLEOPATRA programming language. CLEOPATRA features a C-like imperative syntax for the description of computation, which makes it easier to incorporate in applications already using C. It is event-driven, and thus appropriate for embedded process control applications. It is object-oriented and compositional, thus advocating modularity and reusability. CLEOPATRA is semantically sound; its objects can be transformed, mechanically and unambiguously, into formal TRA automata for verification purposes, which can be pursued using model-checking or theorem proving techniques. Since 1989, an ancestor of CLEOPATRA has been in use as a specification and simulation language for embedded time-critical robotic processes.Harvard University; DARPA (N00039-88-C-0163

Revisiting Waiting Times in DNA evolution

Transcription factors are short stretches of DNA (or $k$-mers) mainly located in promoters sequences that enhance or repress gene expression. With respect to an initial distribution of letters on the DNA alphabet, Behrens and Vingron consider a random sequence of length $n$ that does not contain a given $k$-mer or word of size $k$. Under an evolution model of the DNA, they compute the probability $\mathfrak{p}_n$ that this $k$-mer appears after a unit time of 20 years. They prove that the waiting time for the first apparition of the $k$-mer is well approximated by $T_n=1/\mathfrak{p}_n$. Their work relies on the simplifying assumption that the $k$-mer is not self-overlapping. They observe in particular that the waiting time is mostly driven by the initial distribution of letters. Behrens et al. use an approach by automata that relaxes the assumption related to words overlaps. Their numerical evaluations confirms the validity of Behrens and Vingron approach for non self-overlapping words, but provides up to 44% corrections for highly self-overlapping words such as $\mathtt{AAAAA}$. We devised an approach of the problem by clump analysis and generating functions; this approach leads to prove a quasi-linear behaviour of $\mathfrak{p}_n$ for a large range of values of $n$, an important result for DNA evolution. We present here this clump analysis, first by language decomposition, and next by an automaton construction; finally, we describe an equivalent approach by construction of Markov automata.Comment: 19 pages, 3 Figures, 2 Table