Degree of Sequentiality of Weighted Automata

Weighted automata (WA) are an important formalism to describe quantitative properties. Obtaining equivalent deterministic machines is a longstanding research problem. In this paper we consider WA with a set semantics, meaning that the semantics is given by the set of weights of accepting runs. We focus on multi-sequential WA that are defined as finite unions of sequential WA. The problem we address is to minimize the size of this union. We call this minimum the degree of sequentiality of (the relation realized by) the WA. For a given positive integer k, we provide multiple characterizations of relations realized by a union of k sequential WA over an infinitary finitely generated group: a Lipschitz-like machine independent property, a pattern on the automaton (a new twinning property) and a subclass of cost register automata. When possible, we effectively translate a WA into an equivalent union of k sequential WA. We also provide a decision procedure for our twinning property for commutative computable groups thus allowing to compute the degree of sequentiality. Last, we show that these results also hold for word transducers and that the associated decision problem is PSPACE -complete

Regular Expressions and Transducers over Alphabet-invariant and User-defined Labels

We are interested in regular expressions and transducers that represent word relations in an alphabet-invariant way---for example, the set of all word pairs u,v where v is a prefix of u independently of what the alphabet is. Current software systems of formal language objects do not have a mechanism to define such objects. We define transducers in which transition labels involve what we call set specifications, some of which are alphabet invariant. In fact, we give a more broad definition of automata-type objects, called labelled graphs, where each transition label can be any string, as long as that string represents a subset of a certain monoid. Then, the behaviour of the labelled graph is a subset of that monoid. We do the same for regular expressions. We obtain extensions of a few classic algorithmic constructions on ordinary regular expressions and transducers at the broad level of labelled graphs and in such a way that the computational efficiency of the extended constructions is not sacrificed. For regular expressions with set specs we obtain the corresponding partial derivative automata. For transducers with set specs we obtain further algorithms that can be applied to questions about independent regular languages, in particular the witness version of the independent property satisfaction question

Understanding mixed sequence DNA recognition by novel designed compounds: the kinetic and thermodynamic behavior of azabenzimidazole diamidines

Sequence-specific recognition of DNA by small organic molecules offers a potentially effective approach for the external regulation of gene expression and is an important goal in cell biochemistry. Rational design of compounds from established modules can potentially yield compounds that bind strongly and selectively with specific DNA sequences. An initial approach is to start with common A·T bp recognition molecules and build in G·C recognition units. Here we report on the DNA interaction of a synthetic compound that specifically binds to a G·C bp in the minor groove of DNA by using an azabenzimidazole moiety. The detailed interactions were evaluated with biosensor-surface plasmon resonance (SPR), isothermal calorimetric (ITC), and mass spectrometry (ESI-MS) methods. The compound, DB2277, binds with single G·C bp containing sequences with subnanomolar potency and displays slow dissociation kinetics and high selectivity. A detailed thermodynamic and kinetic study at different experimental salt concentrations and temperatures shows that the binding free energy is salt concentration dependent but essentially temperature independent under our experimental conditions, and binding enthalpy is temperature dependent but salt concentration independent. The results show that in the proper compound structural context novel heterocyclic cations can be designed to strongly recognize complex DNA sequences

Streptococcal cell wall-induced systemic disease. Beneficial effects of trans-bis(5-amidino-2-benzimidazolyl)ethene, a novel, macrophage-directed anti-inflammatory agent.

Previously bis(5-amidino-2-benzimidazolyl)methane (BABIM) was identified as a strong inhibitor of the multisystem inflammatory disease induced in Lewis rats by injection of streptococcus group A cell wall-derived peptidoglycan polysaccharide (PG-APS). A BABIM derivative, trans-bis(5-amidino-2-benzimidazolyl)ethene (BBE), has attracted attention because of striking qualitative and quantitative differences in its activities when compared with the parent compound. BBE could control destructive tibial osteitis and necrotizing granulomatous splenitis and hepatitis, regardless if given in a preventive or curative mode. The compound had little effect on synovitis, however. BABIM, on the other hand, was active against synovitis and osteitis, but not against splenic granuloma formation. To be effective, it needed to be applied in a preventive mode. BBE caused a characteristic enlargement of PG-APS-laden splenic and hepatic macrophages suggesting that those cells represent targets of the inhibitor. BBE may be a powerful tool for the study of granulomatous lesions

Metabolic N-hydroxylation of pentamidine in vitro.

By using high-performance liquid chromatography, the in vitro conversion of pentamidine to the corresponding amidoximes (N-hydroxypentamidine and N,N'-dihydroxypentamidine) was studied in supernatants of rat liver homogenate centrifuged at 9,000 x g. The presence of the two amidoxime peaks in chromatograms was confirmed by liquid secondary ion mass spectrometry and by unequivocal synthesis of the suspected metabolites. The metabolic reactions were found to be catalyzed by the cytochrome P-450 system (mixed-function oxidases). The formation of the monohydroxylated product was found to have a Km of 0.48 mM and a Vmax of 29.50 pmol/min per mg of protein, while the dihydroxylated metabolite had a Km of 0.73 mM and a Vmax of 4.10 pmol/min per mg of protein. N,N'-Dihydroxypentamidine was found to have highly reduced antiprotozoal activity in vitro relative to that of pentamidine, and neither of the hydroxylated metabolites nor pentamidine was found to be significantly mutagenic by the Ames test. Contrary to previous reports, pentamidine is readily metabolized to at least two hydroxylated products, and this conversion may be relevant to the clinical use of the compound and to future drug design

Kleene Theorems for Synchronous Products with Matching

In earlier work [LMP11], we showed that a graph-theoretic condition called “structural cyclicity” enables us to extract syntax from a conflict-equivalent product system of automata. In this paper we have a “pairing” property in our syntax which allows us to connect to a broader class of synchronous product systems [Arn94] with a “matching” property, where the conflict-equivalence is not statically fixed. These systems have been related to labelled free choice nets

From Two-Way Transducers to Regular Function Expressions

International audienceTransducers constitute a fundamental extension of automata. The class of regular word functions has recently emerged as an important class of word-to-word functions, characterized by means of (functional, or unambiguous, or deterministic) two-way transducers, copyless streaming string transducers, and MSO-definable graph transformations. A fundamental result in language theory is Kleene’s Theorem, relating finite state automata and regular expressions. In [3], the authors introduced a set of regular function expressions and proved a similar result for regular word functions, by showing the equivalence with copyless streaming string transducers. In this paper, we propose a direct, simplified and effective translation from unambiguous two-way transducers to regular function expressions extending the Brzozowski and McCluskey algorithm. In addition, we identify a subset of regular function expressions characterizing the (strict) subclass of functional sweeping transducers

How expressions can code for automata

International audienc

The reuse of biosolids on agricultural land: Critical issues and perspective

The sludge management represents a considerable amount of operational costs for wastewater treatment plants (WWTPs). Issues concerning the treatment and the recovery/disposal of biosolids are gaining importance especially in Lombardy region, where the biosolid landspreading on agricultural soils is a very common practice. The aim of this work was to evaluate the results obtained from a survey carried out on the biosolids/sludge, derived from WWTPs, ingoing to and outgoing from the STPs (sludge treatment plants-authorized for the treatment on behalf of third parties) located in Pavia Province. Moreover, the characterization of agricultural soils that receive the biosolids is carried out. Furthermore, the whole biosolid management chain, from production to landspreading on agricultural soils, was studied, highlighting the critical issues based on the survey results. The results obtained suggested the following actions: (a) the reduction of sludge production in WWTPs; (b) a more "controlled" production in terms of biosolid qualitative characteristics; (c) better "selection" of the sludge ingoing to STPs; and (d) more effective actions to control the "response" of the agricultural soils. Furthermore, full compliance with the best spreading practices on the soils is required, as well as a better use of agronomic skills to obtain a higher resource valorization. PRACTITIONER POINTS: In this work, the characteristics of biosolid spread in agricultural soils in Pavia Province were analyzed. The minimization of sludge production in WWTPs is encouraged in order to reduce critical issues related to biosolid management. The stabilization process in WWTPs should improve in order to obtain a better quality sludge. A better "selection" of the sludge ingoing to STPs and a more effective monitoring of the agricultural soils are encouraged