Using contracted solution graphs for solving reconfiguration problems.

We introduce a dynamic programming method for solving reconfiguration problems, based on contracted solution graphs, which are obtained from solution graphs by performing an appropriate series of edge contractions that decrease the graph size without losing any critical information needed to solve the reconfiguration problem under consideration. As an example, we consider a well-studied problem: given two k-colorings alpha and beta of a graph G, can alpha be modified into beta by recoloring one vertex of G at a time, while maintaining a k-coloring throughout? By applying our method in combination with a thorough exploitation of the graph structure we obtain a polynomial-time algorithm for (k-2)-connected chordal graphs

Stably computing order statistics with arithmetic population protocols.

In this paper we initiate the study of populations of agents with very limited capabilities that are globally able to compute order statistics of their arithmetic input values via pair-wise meetings. To this extent, we introduce the Arithmetic Population Protocol (APP) model, embarking from the well known Population Protocol (PP) model and inspired by two recent papers in which states are treated as integer numbers. In the APP model, every agent has a state from a set Q of states, as well as a fixed number of registers (independent of the size of the population), each of which can store an element from a totally ordered set S of samples. Whenever two agents interact with each other, they update their states and the values stored in their registers according to a joint transition function. This transition function is also restricted; it only allows (a) comparisons and (b) copy / paste operations for the sample values that are stored in the registers of the two interacting agents. Agents can only meet in pairs via a fair scheduler and are required to eventually converge to the same output value of the function that the protocol globally and stably computes. We present two different APPs for stably computing the median of the input values, initially stored on the agents of the population. Our first APP, in which every agent has 3 registers and no states, stably computes (with probability 1) the median under any fair scheduler in any strongly connected directed (or connected undirected) interaction graph. Under the probabilistic scheduler, we show that our protocol stably computes the median in O(n^6) number of interactions in a connected undirected interaction graph of $n$ agents. Our second APP, in which every agent has 2 registers and O(n^2 log{n}) states, computes to the correct median of the input with high probability in O(n^3 log{n}) interactions, assuming the probabilistic scheduler and the complete interaction graph. Finally we present a third APP which, for any k, stably computes the k-th smallest element of the input of the population under any fair scheduler and in any strongly connected directed (or connected undirected) interaction graph. In this APP every agent has 2 registers and n states. Upon convergence every agent has a different state; all these states provide a total ordering of the agents with respect to their input values

Absorbing Subalgebras, Cyclic Terms, and the Constraint Satisfaction Problem

The Algebraic Dichotomy Conjecture states that the Constraint Satisfaction Problem over a fixed template is solvable in polynomial time if the algebra of polymorphisms associated to the template lies in a Taylor variety, and is NP-complete otherwise. This paper provides two new characterizations of finitely generated Taylor varieties. The first characterization is using absorbing subalgebras and the second one cyclic terms. These new conditions allow us to reprove the conjecture of Bang-Jensen and Hell (proved by the authors) and the characterization of locally finite Taylor varieties using weak near-unanimity terms (proved by McKenzie and Mar\'oti) in an elementary and self-contained way

Expressive Equivalence and Succinctness of Parametrized Automata with respect to Finite Memory Automata

International audienceWe compare parametrized automata, a class of automata recently introduced by the authors, against finite memory automata with non-deterministic assignment, an existing class of automata used to model services. We prove that both classes have the same expressive power, while parametrized automata can be exponentially succinct in some cases. We then prove that deciding simulation preorder for parametrized automata is EXPTIME-complete, extending an earlier result showing it in EXPTIME

The many facets of string transducers

Regular word transductions extend the robust notion of regular languages from a qualitative to a quantitative reasoning. They were already considered in early papers of formal language theory, but turned out to be much more challenging. The last decade brought considerable research around various transducer models, aiming to achieve similar robustness as for automata and languages. In this paper we survey some older and more recent results on string transducers. We present classical connections between automata, logic and algebra extended to transducers, some genuine definability questions, and review approaches to the equivalence problem

Equivalence of finite-valued streaming string transducers is decidable

In this paper we provide a positive answer to a question left open by Alur and and Deshmukh in 2011 by showing that equivalence of finite-valued copyless streaming string transducers is decidable

Propositional Dynamic Logic for Message-Passing Systems

We examine a bidirectional propositional dynamic logic (PDL) for finite and infinite message sequence charts (MSCs) extending LTL and TLC-. By this kind of multi-modal logic we can express properties both in the entire future and in the past of an event. Path expressions strengthen the classical until operator of temporal logic. For every formula defining an MSC language, we construct a communicating finite-state machine (CFM) accepting the same language. The CFM obtained has size exponential in the size of the formula. This synthesis problem is solved in full generality, i.e., also for MSCs with unbounded channels. The model checking problem for CFMs and HMSCs turns out to be in PSPACE for existentially bounded MSCs. Finally, we show that, for PDL with intersection, the semantics of a formula cannot be captured by a CFM anymore

Trastuzumab-associated cardiac adverse effects in the Herceptin adjuvant trial.

PURPOSE: The purpose of this analysis was to investigate trastuzumab-associated cardiac adverse effects in breast cancer patients after completion of (neo)adjuvant chemotherapy with or without radiotherapy. PATIENTS AND METHODS: The Herceptin Adjuvant (HERA) trial is a three-group, multicenter, open-label randomized trial that compared 1 or 2 years of trastuzumab given once every 3 weeks with observation in patients with HER-2-positive breast cancer. Only patients who after completion of (neo)adjuvant chemotherapy with or without radiotherapy had normal left ventricular ejection fraction (LVEF > or = 55%) were eligible. A repeat LVEF assessment was performed in case of cardiac dysfunction. RESULTS: Data were available for 1,693 patients randomly assigned to 1 year trastuzumab and 1,693 patients randomly assigned to observation. The incidence of trastuzumab discontinuation due to cardiac disorders was low (4.3%). The incidence of cardiac end points was higher in the trastuzumab group compared with observation (severe congestive heart failure [CHF], 0.60% v 0.00%; symptomatic CHF, 2.15% v 0.12%; confirmed significant LVEF drops, 3.04% v 0.53%). Most patients with cardiac dysfunction recovered in fewer than 6 months. Patients with trastuzumab-associated cardiac dysfunction were treated with higher cumulative doses of doxorubicin (287 mg/m(2) v 257 mg/m(2)) or epirubicin (480 mg/m(2) v 422 mg/m(2)) and had a lower screening LVEF and a higher body mass index. CONCLUSION: Given the clear benefit in disease-free survival, the low incidence of cardiac adverse events, and the suggestion that cardiac dysfunction might be reversible, adjuvant trastuzumab should be considered for treatment of breast cancer patients who fulfill the HERA trial eligibility criteri

One-way definability of sweeping transducers

Two-way finite-state transducers on words are strictly more expressive than one-way transducers. It has been shown recently how to decide if a two-way functional transducer has an equivalent one-way transducer, and the complexity of the algorithm is non-elementary. We propose an alternative and simpler characterization for sweeping functional transducers, namely, for transducers that can only reverse their head direction at the extremities of the input. Our algorithm works in 2EXPSPACE and, in the positive case, produces an equivalent one-way transducer of doubly exponential size. We also show that the bound on the size of the transducer is tight, and that the one-way definability problem is undecidable for (sweeping) non-functional transducers

One-way definability of two-way word transducers

Functional transductions realized by two-way transducers (or, equally, by streaming transducers or MSO transductions) are the natural and standard notion of `regular' mappings from words to words. It was shown in 2013 that it is decidable if such a transduction can be implemented by some one-way transducer, but the given algorithm has non-elementary complexity. We provide an algorithm of different flavor solving the above question, that has doubly exponential space complexity. In the special case of sweeping transducers the complexity is one exponential less. We also show how to construct an equivalent one-way transducer, whenever it exists, in doubly or triply exponential time, again depending on whether the input transducer is sweeping or two-way. In the sweeping case our construction is shown to be optimal