On the Complexity of Heterogeneous Multidimensional Games

We study two-player zero-sum turn-based games played on multidimensional weighted graphs with heterogeneous quantitative objectives. Our objectives are defined starting from the measures Inf, Sup, LimInf, and LimSup of the weights seen along the play, as well as on the window mean-payoff (WMP) measure recently introduced in [Krishnendu,Doyen,Randour,Raskin, Inf. Comput., 2015]. Whereas multidimensional games with Boolean combinations of classical mean-payoff objectives are undecidable [Velner, FOSSACS, 2015], we show that CNF/DNF Boolean combinations for heterogeneous measures taken among {WMP, Inf, Sup, LimInf, LimSup} lead to EXPTIME-completeness with exponential memory strategies for both players. We also identify several interesting fragments with better complexities and memory requirements, and show that some of them are solvable in PTIME

Pigmentation and Vitamin D Metabolism in Caucasians: Low Vitamin D Serum Levels in Fair Skin Types in the UK

Background: Vitamin D may play a protective role in many diseases. Public health messages are advocating sun avoidance to reduce skin cancer risk but the potential deleterious effects of these recommendations for vitamin D metabolism have been poorly investigated. Methodology/Principal Findings: We investigated the association between 25-hydroxy-vitamin D (25(OH)D), skin type and ultraviolet exposure in 1414 Caucasian females in the UK. Mean age of the cohort was 47 years (18–79) and mean 25(OH)D levels were 77 nmol/L (6–289). 25(OH)D levels were strongly associated with season of sampling with higher levels in the spring and summer months (p,0.0001). Light skin types (skin type 1 and 2) have lower levels of 25(OH)D (mean 71 nmol/L) compared to darker skin types (skin type 3 and 4) (mean 82 nmol/L) after adjusting for multiple confounders (p,0.0001). The trend for increasing risk of low vitamin D with fairer skin types was highly significant despite adjustment for all confounders (p = 0.001). Conclusions/Significance: Contrary to previous studies across different ethnic backgrounds, this study within Caucasian UK females shows that fair skin types have lower levels of 25(OH)D compared to darker skin types with potential detrimental health effects. Public health campaigns advocating sun avoidance in fair skinned individuals may need to be revised in vie

Pigmentation and Vitamin D Metabolism in Caucasians: Low Vitamin D Serum Levels in Fair Skin Types in the UK

Background: Vitamin D may play a protective role in many diseases. Public health messages are advocating sun avoidance to reduce skin cancer risk but the potential deleterious effects of these recommendations for vitamin D metabolism have been poorly investigated. Methodology/Principal Findings: We investigated the association between 25-hydroxy-vitamin D (25(OH)D), skin type and ultraviolet exposure in 1414 Caucasian females in the UK. Mean age of the cohort was 47 years (18–79) and mean 25(OH)D levels were 77 nmol/L (6–289). 25(OH)D levels were strongly associated with season of sampling with higher levels in the spring and summer months (p,0.0001). Light skin types (skin type 1 and 2) have lower levels of 25(OH)D (mean 71 nmol/L) compared to darker skin types (skin type 3 and 4) (mean 82 nmol/L) after adjusting for multiple confounders (p,0.0001). The trend for increasing risk of low vitamin D with fairer skin types was highly significant despite adjustment for all confounders (p = 0.001). Conclusions/Significance: Contrary to previous studies across different ethnic backgrounds, this study within Caucasian UK females shows that fair skin types have lower levels of 25(OH)D compared to darker skin types with potential detrimental health effects. Public health campaigns advocating sun avoidance in fair skinned individuals may need to be revised in vie

Real-Time Model-Checking: Parameters everywhere

In this paper, we study the model-checking and parameter synthesis problemsof the logic TCTL over discrete-timed automata where parameters are allowedboth in the model (timed automaton) and in the property (temporal formula). Ourresults are as follows. On the negative side, we show that the model-checkingproblem of TCTL extended with parameters is undecidable over discrete-timedautomata with only one parametric clock. The undecidability result needsequality in the logic. On the positive side, we show that the model-checkingand the parameter synthesis problems become decidable for a fragment of thelogic where equality is not allowed. Our method is based on automata theoreticprinciples and an extension of our method to express durations of runs in timedautomata using Presburger arithmetic

Real-Time Model-Checking: Parameters everywhere

In this paper, we study the model-checking and parameter synthesis problems of the logic TCTL over discrete-timed automata where parameters are allowed both in the model (timed automaton) and in the property (temporal formula). Our results are as follows. On the negative side, we show that the model-checking problem of TCTL extended with parameters is undecidable over discrete-timed automata with only one parametric clock. The undecidability result needs equality in the logic. On the positive side, we show that the model-checking and the parameter synthesis problems become decidable for a fragment of the logic where equality is not allowed. Our method is based on automata theoretic principles and an extension of our method to express durations of runs in timed automata using Presburger arithmetic

On the Sets of Real Numbers Recognized by Finite Automata in Multiple Bases

This article studies the expressive power of finite automata recognizing sets of real numbers encoded in positional notation. We consider Muller automata as well as the restricted class of weak deterministic automata, used as symbolic set representations in actual applications. In previous work, it has been established that the sets of numbers that are recognizable by weak deterministic automata in two bases that do not share the same set of prime factors are exactly those that are definable in the first order additive theory of real and integer numbers. This result extends Cobham's theorem, which characterizes the sets of integer numbers that are recognizable by finite automata in multiple bases. In this article, we first generalize this result to multiplicatively independent bases, which brings it closer to the original statement of Cobham's theorem. Then, we study the sets of reals recognizable by Muller automata in two bases. We show with a counterexample that, in this setting, Cobham's theorem does not generalize to multiplicatively independent bases. Finally, we prove that the sets of reals that are recognizable by Muller automata in two bases that do not share the same set of prime factors are exactly those definable in the first order additive theory of real and integer numbers. These sets are thus also recognizable by weak deterministic automata. This result leads to a precise characterization of the sets of real numbers that are recognizable in multiple bases, and provides a theoretical justification to the use of weak automata as symbolic representations of sets

The Reactive Synthesis Competition (SYNTCOMP): 2018-2021

We report on the last four editions of the reactive synthesis competition (SYNTCOMP 2018-2021). We briefly describe the evaluation scheme and the experimental setup of SYNTCOMP. Then, we introduce new benchmark classes that have been added to the SYNTCOMP library and give an overview of the participants of SYNTCOMP. Finally, we present and analyze the results of our experimental evaluations, including a ranking of tools with respect to quantity and quality of solutions