Crisp-determinization of weighted tree automata over strong bimonoids

We consider weighted tree automata (wta) over strong bimonoids and their initial algebra semantics and their run semantics. There are wta for which these semantics are different; however, for bottom-up deterministic wta and for wta over semirings, the difference vanishes. A wta is crisp-deterministic if it is bottom-up deterministic and each transition is weighted by one of the unit elements of the strong bimonoid. We prove that the class of weighted tree languages recognized by crisp-deterministic wta is the same as the class of recognizable step mappings. Moreover, we investigate the following two crisp-determinization problems: for a given wta ${\cal A}$, (a) does there exist a crisp-deterministic wta which computes the initial algebra semantics of ${\cal A}$ and (b) does there exist a crisp-deterministic wta which computes the run semantics of ${\cal A}$? We show that the finiteness of the Nerode algebra ${\cal N}({\cal A})$ of ${\cal A}$ implies a positive answer for (a), and that the finite order property of ${\cal A}$ implies a positive answer for (b). We show a sufficient condition which guarantees the finiteness of ${\cal N}({\cal A})$ and a sufficient condition which guarantees the finite order property of ${\cal A}$. Also, we provide an algorithm for the construction of the crisp-deterministic wta according to (a) if ${\cal N}({\cal A})$ is finite, and similarly for (b) if ${\cal A}$ has finite order property. We prove that it is undecidable whether an arbitrary wta ${\cal A}$ is crisp-determinizable. We also prove that both, the finiteness of ${\cal N}({\cal A})$ and the finite order property of ${\cal A}$ are undecidable.

Historical stages of development of the mechanism of state regulation of the institution of adoption

The article considers adoption as one of the oldest social institutions. The mechanism of state regulation of the institution ofadoption has a long history of formation and development. During the historical development of the institution of adoption, thiscategory of concepts has been improved, acquired new meaning and justification.In the primitive communal system, in order to survive, people had to stick together, work collectively and raise children together.Therefore, it was believed that in such a society, orphanhood did not exist.The institution of adoption as a social phenomenon is characterized by its customs and traditions, but its development andformation as a social institution are ambiguous and depend on the level of development of society, national characteristics andprevailing relations in society.The development and formation of the mechanism of state regulation of the institution of adoption can be traced back to ancientRome. Adoption was extremely widely used and took various social forms. Over the centuries, different peoples have changed the goals,conditions, order, property and non-property consequences of the adoption of another’s child, and sometimes adults. This was due tovarious purposes, which were determined by the historical, religious, social and political conditions of society at one or another stageof its development.The formation of the mechanism of state regulation of the institution of adoption in the times of Kievan Rus was taking intoaccount customary law. On the basis of customary law, the first legal norms on adoption in the collection of ancient Russian law“Russian Truth” are formed.The period of the Grand Duchy of Lithuania and the Commonwealth is characterized by the legal status of the child in the threeLithuanian statutes. Significant changes in the improvement of the care system took place during the reign of Catherine II.In Soviet times, the development of the mechanism of state regulation of the institution of adoption in Ukraine began with theadoption of legislation, the rules of which regulated the institution of adoption. During Ukraine’s independence, there were changes inthe mechanism of state regulation of the institution of adoption.Traditions, customs and rites, historical experience in regulating adoption relations show that they have become a core for theUkrainian state to create its own legal framework in the field of adoption.

Probabilities of first-order sentences on sparse random relational structures: an application to definability on random CNF formulas

We extend the convergence law for sparse random graphs proven by Lynch to arbitrary relational languages. We consider a finite relational vocabulary $\sigma $ and a first-order theory $T$ for $\sigma $ composed of symmetry and anti-reflexivity axioms. We define a binomial random model of finite $\sigma $-structures that satisfy $T$ and show that first-order properties have well defined asymptotic probabilities when the expected number of tuples satisfying each relation in $\sigma $ is linear. It is also shown that these limit probabilities are well behaved with respect to several parameters that represent the density of tuples in each relation $R$ in the vocabulary $\sigma $. An application of these results to the problem of random Boolean satisfiability is presented. We show that in a random $k$-CNF formula on $n$ variables, where each possible clause occurs with probability $\sim c/n^{k-1}$, independently any first-order property of $k$-CNF formulas that implies unsatisfiability does almost surely not hold as $n$ tends to infinity.

Pseudofinite difference fields and counting dimensions

We study a family of ultraproducts of finite fields with the Frobenius automorphism in this paper. Their theories have the strict order property and TP2. But the coarse pseudofinite dimension of the definable sets is definable and integer-valued. Moreover, we also discuss the possible connection between coarse dimension and transformal transcendence degree in these difference fields.

Noun/pronoun asymmetry in Polish: Against the nominal perspective and the DP-hypothesis

This paper argues that the Polish noun-pronoun asymmetry in which the intensifier sam ‘self’ precedes nouns and follows pronominals is not a simple case of configuration in the DP, whereby pronouns, unlike nominals, target D0 for referential reasons (cf. Rutkowski 2002, 2012). Such viewpoints, in the case of Polish, are unfortunate because they appear to underlyingly work on and draw from the syntax of nominal projections characteristic of English or Italian i.e., languages with articles. We show that the asymmetry pertains to various semantic interpretations of sam, the different semantic specification of nominals and pronominals, and the flexible word order property. What we need, therefore, is a broader clausal perspective coupled with necessary remarks on the abovementioned issues. Thus, rather than employing the DP-hypothesis, we assume two cornerstone phenomena i.e. flexible word order and rich agreement to be crucial here as they facilitate syntactic options like focalisation or topicalisation which manifest discourse information and in which sam functions as a focus or topic particle (cf. Constantinou 2014). These contexts are held typical of the asymmetry, thereby making it an interplay between semantic properties of nominal/pronominal expressions and organisation of discourse information that syntax makes available.

Pseudofinite difference fields

We study a family of ultraproducts of finite fields with the Frobenius automorphism in this paper. Their theories have the strict order property and TP2. But the coarse pseudofinite dimension of the definable sets is definable and integer-valued. Moreover, we establish a partial connection between coarse dimension and transformal transcendence degree in these difference fields.

The Predicate of Existence

Kant famously declared that existence is not a (real) predicate. This famous dictum has been seen as echoed in the doctrine of the founders of modern logic, Gottlob Frege and Bertrand Russell, that existence isn’t a first-order property possessed by individuals, but rather a second-order property expressed by the existential quantifier. Russell in 1905 combined this doctrine with his new theory of descriptions and declared the paradox of nonexistence to be resolved without resorting to his earlier distinction between existence and being. In recent years, however, logicians and philosophers like Saul Kripke, David Kaplan, and Nathan Salmon have argued that there is no defensible reason to deny that existence is a property of individuals. Kant’s dictum has also been re-evaluated, the result being that the paradox of nonexistence has not, after all, disappeared. Yet it’s not clear how exactly Kripke et al. propose to resolve the paradox.

Materiālā sastāva problemātika administratīvo sodu kontekstā

Pievēršoties diskusijai par Administratīvās atbildības likumu un administratīvo pārkāpumu sastāvu iekļaušanu nozares normatīvajos aktos, jāņem vērā, ka jebkura administratīvā pārkāpuma kvalifikācijas pamatā ir administratīvā pārkāpuma sastāva konstatēšana. Proti, jākonstatē objektīvo un subjektīvo pazīmju kopums – administratīvā pārkāpuma objekts, objektīvā puse, subjekts un subjektīvā puse. Materiālā sastāva objektīvās puses pierādīšanai nepieciešams konstatēt ne tikai subjekta darbību vai bezdarbību, bet arī sekas un cēloņsakarību. Šis administratīvās atbildības piemērošanas nosacījums saistīts ar vairākiem teorētiskiem un praktiskiem problēmjautājumiem. Šā raksta mērķis – izanalizēt materiālā sastāva jautājumu Latvijas Republikas administratīvo sodu reformas kontekstā. Problēmjautājumu analīzes rezultātā tika secināts, ka administratīvās atbildības piemērošanai nozares normatīvajos aktos būtu jāiekļauj vienīgi formālie sastāvi. Turklāt nav iespējama automātiska pašreizējo materiālo sastāvu transformēšana formālajos sastāvos. Ja Latvijas administratīvo pārkāpumu kodeksā iekļautā materiālā sastāva sekas likumdevējs vairs neplāno uzsvērt kā sastāva pazīmi, tad šis sastāvs nozares likumos nav jāpārņem. Gadījumā, ja nozares normatīvajos aktos tomēr tiks pārņemti šobrīd spēkā esošie materiālie sastāvi, praksē neizdosies realizēt plānoto atteikšanos no vainas kā administratīvās atbildības priekšnoteikuma, aizstājot to ar vainojamības konceptu. Mūsdienu administratīvajai justīcijai vajadzētu atteikties no ārkārtīgi detalizēta regulējuma, pārmērīgas kontroles un represīvās sodīšanas. Administratīvās atbildības pamatmērķis ir adekvātu rezultātu sasniegšana vispārējā un individuālajā prevencijā, tāpēc gadījumos, kuros iespējama lietderīga alternatīva, administratīvos sodus nevajadzētu piemērot. Pētījums ir balstīts uz ārvalstu zinātnisko literatūru un tiesu judikatūru. Pētījuma rezultātus var izmantot gan nozares teorētiķi, gan arī praktiķi. The article aims to discuss problems of materially defined violation in the context of administrative sanctions. The task of administrative violations legislation is to protect public order, property, socio-economic, political and personal rights and freedoms of citizens, to prevent right violations, to educate citizens in a spirit of precise and strict observance of laws, to inculcate a full of respect attitude in them towards the rights of other citizens, honour and self-esteem towards the provisions of social life, upright attitude towards the duties thereof and liability to the public. For the implementation of this task, administrative violation shall be acknowledged as an unlawful, blameable (committed with intent or through negligence) action or inaction and regarding which administrative liability is specified in the Law. The article analyses not only the legal aspect of the materially defined violation, but also the essence of the term “formally defined violation”. This article outlines the problems related to administrative sanctions and it analyses the attempts of the legislator to improve laws and regulations in the field of administrative justice.