Two-Way Parikh Automata

Parikh automata extend automata with counters whose values can only be tested at the end of the computation, with respect to membership into a semi-linear set. Parikh automata have found several applications, for instance in transducer theory, as they enjoy a decidable emptiness problem. In this paper, we study two-way Parikh automata. We show that emptiness becomes undecidable in the non-deterministic case. However, it is PSpace-C when the number of visits to any input position is bounded and the semi-linear set is given as an existential Presburger formula. We also give tight complexity bounds for the inclusion, equivalence and universality problems. Finally, we characterise precisely the complexity of those problems when the semi-linear constraint is given by an arbitrary Presburger formula

Safety and Liveness of Quantitative Automata

The safety-liveness dichotomy is a fundamental concept in formal languages which plays a key role in verification. Recently, this dichotomy has been lifted to quantitative properties, which are arbitrary functions from infinite words to partially-ordered domains. We look into harnessing the dichotomy for the specific classes of quantitative properties expressed by quantitative automata. These automata contain finitely many states and rational-valued transition weights, and their common value functions Inf, Sup, LimInf, LimSup, LimInfAvg, LimSupAvg, and DSum map infinite words into the totally-ordered domain of real numbers. In this automata-theoretic setting, we establish a connection between quantitative safety and topological continuity and provide an alternative characterization of quantitative safety and liveness in terms of their boolean counterparts. For all common value functions, we show how the safety closure of a quantitative automaton can be constructed in PTime, and we provide PSpace-complete checks of whether a given quantitative automaton is safe or live, with the exception of LimInfAvg and LimSupAvg automata, for which the safety check is in ExpSpace. Moreover, for deterministic Sup, LimInf, and LimSup automata, we give PTime decompositions into safe and live automata. These decompositions enable the separation of techniques for safety and liveness verification for quantitative specifications

Regular Methods for Operator Precedence Languages

The operator precedence languages (OPLs) represent the largest known subclass of the context-free languages which enjoys all desirable closure and decidability properties. This includes the decidability of language inclusion, which is the ultimate verification problem. Operator precedence grammars, automata, and logics have been investigated and used, for example, to verify programs with arithmetic expressions and exceptions (both of which are deterministic pushdown but lie outside the scope of the visibly pushdown languages). In this paper, we complete the picture and give, for the first time, an algebraic characterization of the class of OPLs in the form of a syntactic congruence that has finitely many equivalence classes exactly for the operator precedence languages. This is a generalization of the celebrated Myhill-Nerode theorem for the regular languages to OPLs. As one of the consequences, we show that universality and language inclusion for nondeterministic operator precedence automata can be solved by an antichain algorithm. Antichain algorithms avoid determinization and complementation through an explicit subset construction, by leveraging a quasi-order on words, which allows the pruning of the search space for counterexample words without sacrificing completeness. Antichain algorithms can be implemented symbolically, and these implementations are today the best-performing algorithms in practice for the inclusion of finite automata. We give a generic construction of the quasi-order needed for antichain algorithms from a finite syntactic congruence. This yields the first antichain algorithm for OPLs, an algorithm that solves the ExpTime-hard language inclusion problem for OPLs in exponential time

LIPIcs

A regular language L of finite words is composite if there are regular languages L₁,L₂,…,L_t such that L = ⋂_{i = 1}^t L_i and the index (number of states in a minimal DFA) of every language L_i is strictly smaller than the index of L. Otherwise, L is prime. Primality of regular languages was introduced and studied in [O. Kupferman and J. Mosheiff, 2015], where the complexity of deciding the primality of the language of a given DFA was left open, with a doubly-exponential gap between the upper and lower bounds. We study primality for unary regular languages, namely regular languages with a singleton alphabet. A unary language corresponds to a subset of ℕ, making the study of unary prime languages closer to that of primality in number theory. We show that the setting of languages is richer. In particular, while every composite number is the product of two smaller numbers, the number t of languages necessary to decompose a composite unary language induces a strict hierarchy. In addition, a primality witness for a unary language L, namely a word that is not in L but is in all products of languages that contain L and have an index smaller than L’s, may be of exponential length. Still, we are able to characterize compositionality by structural properties of a DFA for L, leading to a LogSpace algorithm for primality checking of unary DFAs

LIPIcs

A deterministic finite automaton (DFA) is composite if its language L() can be decomposed into an intersection ⋂_{i = 1}^k L(_i) of languages of smaller DFAs. Otherwise, is prime. This notion of primality was introduced by Kupferman and Mosheiff in 2013, and while they proved that we can decide whether a DFA is composite, the precise complexity of this problem is still open, with a doubly-exponential gap between the upper and lower bounds. In this work, we focus on permutation DFAs, i.e., those for which the transition monoid is a group. We provide an NP algorithm to decide whether a permutation DFA is composite, and show that the difficulty of this problem comes from the number of non-accepting states of the instance: we give a fixed-parameter tractable algorithm with the number of rejecting states as the parameter. Moreover, we investigate the class of commutative permutation DFAs. Their structural properties allow us to decide compositionality in NL, and even in LOGSPACE if the alphabet size is fixed. Despite this low complexity, we show that complex behaviors still arise in this class: we provide a family of composite DFAs each requiring polynomially many factors with respect to its size. We also consider the variant of the problem that asks whether a DFA is k-factor composite, that is, decomposable into k smaller DFAs, for some given integer k ∈ ℕ. We show that, for commutative permutation DFAs, restricting the number of factors makes the decision computationally harder, and yields a problem with tight bounds: it is NP-complete. Finally, we show that in general, this problem is in PSPACE, and it is in LOGSPACE for DFAs with a singleton alphabet

Weighted Transducers for Robustness Verification

Automata theory provides us with fundamental notions such as languages, membership, emptiness and inclusion that in turn allow us to specify and verify properties of reactive systems in a useful manner. However, these notions all yield "yes"/"no" answers that sometimes fall short of being satisfactory answers when the models being analyzed are imperfect, and the observations made are prone to errors. To address this issue, a common engineering approach is not just to verify that a system satisfies a property, but whether it does so robustly. We present notions of robustness that place a metric on words, thus providing a natural notion of distance between words. Such a metric naturally leads to a topological neighborhood of words and languages, leading to quantitative and robust versions of the membership, emptiness and inclusion problems. More generally, we consider weighted transducers to model the cost of errors. Such a transducer models neighborhoods of words by providing the cost of rewriting a word into another. The main contribution of this work is to study robustness verification problems in the context of weighted transducers. We provide algorithms for solving the robust and quantitative versions of the membership and inclusion problems while providing useful motivating case studies including approximate pattern matching problems to detect clinically relevant events in a large type-1 diabetes dataset

Safety and Liveness of Quantitative Automata

The safety-liveness dichotomy is a fundamental concept in formal languages which plays a key role in verification. Recently, this dichotomy has been lifted to quantitative properties, which are arbitrary functions from infinite words to partially-ordered domains. We look into harnessing the dichotomy for the specific classes of quantitative properties expressed by quantitative automata. These automata contain finitely many states and rational-valued transition weights, and their common value functions Inf, Sup, LimInf, LimSup, LimInfAvg, LimSupAvg, and DSum map infinite words into the totally-ordered domain of real numbers. In this automata-theoretic setting, we establish a connection between quantitative safety and topological continuity and provide an alternative characterization of quantitative safety and liveness in terms of their boolean counterparts. For all common value functions, we show how the safety closure of a quantitative automaton can be constructed in PTime, and we provide PSpace-complete checks of whether a given quantitative automaton is safe or live, with the exception of LimInfAvg and LimSupAvg automata, for which the safety check is in ExpSpace. Moreover, for deterministic Sup, LimInf, and LimSup automata, we give PTime decompositions into safe and live automata. These decompositions enable the separation of techniques for safety and liveness verification for quantitative specifications.Comment: Full version of the paper to appear in CONCUR 202

Effect of eplerenone on parathyroid hormone levels in patients with primary hyperparathyroidism: a randomized, double-blind, placebo-controlled trial

<p>Abstract</p> <p>Background</p> <p>Increasing evidence suggests the bidirectional interplay between parathyroid hormone and aldosterone as an important mechanism behind the increased risk of cardiovascular damage and bone disease observed in primary hyperparathyroidism. Our primary object is to assess the efficacy of the mineralocorticoid receptor-blocker eplerenone to reduce parathyroid hormone secretion in patients with parathyroid hormone excess.</p> <p>Methods/design</p> <p>Overall, 110 adult male and female patients with primary hyperparathyroidism will be randomly assigned to eplerenone (25 mg once daily for 4 weeks and 4 weeks with 50 mg once daily after dose titration] or placebo, over eight weeks. Each participant will undergo detailed clinical assessment, including anthropometric evaluation, 24-h ambulatory arterial blood pressure monitoring, echocardiography, kidney function and detailed laboratory determination of biomarkers of bone metabolism and cardiovascular disease.</p> <p>The study comprises the following exploratory endpoints: mean change from baseline to week eight in (1) parathyroid hormone(1–84) as the primary endpoint and (2) 24-h systolic and diastolic ambulatory blood pressure levels, NT-pro-BNP, biomarkers of bone metabolism, 24-h urinary protein/albumin excretion and echocardiographic parameters reflecting systolic and diastolic function as well as cardiac dimensions, as secondary endpoints.</p> <p>Discussion</p> <p>In view of the reciprocal interaction between aldosterone and parathyroid hormone and the potentially ensuing target organ damage, the EPATH trial is designed to determine whether eplerenone, compared to placebo, will effectively impact on parathyroid hormone secretion and improve cardiovascular, renal and bone health in patients with primary hyperparathyroidism.</p> <p>Trial registration</p> <p>ISRCTN33941607</p

Community-Level Responses to Iron Availability in Open Ocean Plankton Ecosystems

Predicting responses of plankton to variations in essential nutrients is hampered by limited in situ measurements, a poor understanding of community composition, and the lack of reference gene catalogs for key taxa. Iron is a key driver of plankton dynamics and, therefore, of global biogeochemical cycles and climate. To assess the impact of iron availability on plankton communities, we explored the comprehensive bio-oceanographic and bio-omics data sets from Tara Oceans in the context of the iron products from two state-of-the-art global scale biogeochemical models. We obtained novel information about adaptation and acclimation toward iron in a range of phytoplankton, including picocyanobacteria and diatoms, and identified whole subcommunities covarying with iron. Many of the observed global patterns were recapitulated in the Marquesas archipelago, where frequent plankton blooms are believed to be caused by natural iron fertilization, although they are not captured in large-scale biogeochemical models. This work provides a proof of concept that integrative analyses, spanning from genes to ecosystems and viruses to zooplankton, can disentangle the complexity of plankton communities and can lead to more accurate formulations of resource bioavailability in biogeochemical models, thus improving our understanding of plankton resilience in a changing environment