On the (un)decidability of a near-unanimity term

We investigate the near-unanimity problem: given a finite algebra, decide if it has a near-unanimity term of finite arity. We prove that it is undecidable of a finite algebra if it has a partial near-unanimity term on its underlying set excluding two fixed elements. On the other hand, based on Rosenberg’s characterization of maximal clones, we present partial results towards proving the decidability of the general problem

Semilattices with a group of automorphisms

We investigate semilattices expanded by a group F of automorphisms acting as new unary basic operations. We describe up to isomorphism all simple algebras of this kind in case that F is commutative. Finally, we present an example of a simple algebra that does not fit in the previous description, if F is not commutative

Gyenge többségi függvények = Weak near-unanimity operations

Az OTKA pályázatom benyújtása (2008. február 11) óta 8 cikkem jelent nemzetközi folyóiratokban, de ezek közül csak kettő cikk született a kutatási programban megadott témában a beszámolási időszak alatt, ezért a többi 6 megjelent cikket nem tüntettem fel a jelentésben. Ezen cikkeken kívül a kutatási tervnek megfelelően további 3 kézirat van publikálásra benyújtva, illetve egy kézirat született, amely nincsen még benyújtva. A kutatási időszakban összesen hat nemzetközi konferencián adtam elő, ezek közül négyen meghívott előadóként. Az [1] cikkben egy irányított fákból álló speciális gráfosztályra, az úgynevezett speciális triádokra bizonyítjuk a homomorfizmus problémára vonatkozó dichotómia sejtés. A [2] cikkben algoritmust adunk arra, hogy láncok direkt szorzatában az azonos elemszámú ideálok melyikében maximális az elemek magasságának összege. A [3] kéziratban a korlátos szélességű és kevés részhatvánnyal rendelkező algebrákra vonatkozó kényszerkielégíthetőségi problémát megoldó algoritmusokat ötvöztem. A [4] kéziratban bebizonyítottuk a Valeriote sejtést reflexív irányított gráfokra. Az [5] kéziratban a Valeriote sejtés több ekvivalens megfogalmazását adtuk meg. A [6] kéziratban a CSP probléma egy teljesen új redukcióját vezettük be, amely segítségével újabb algebraosztályokra bizonyítható a dichotómia sejtés. | Since the submission of my OTKA grant proposal (2008/08/11) I had eight articles appeared in international journals, but only two of them were on a topic listed in the project proposal. Therefore, I did not mention the other 6 in this report. Beside these articles I have 3 submitted manuscripts and one manuscript not jet submitted. During the three years of this research grant I have given 6 talks on international conferences, four of them were invited plenary talks. In [1] we have proved the constraint satisfaction dichotomy conjecture for a special class of directed trees, for the class of special triads. In [2] we give an algorithm to determine the order ideal of a direct product of chains in which the number of elements equals a fixed integer and the sum of heights of elements is maximal. In [3] I have combined the algorithms solving the constraint satisfaction problem for bounded width algebras and for algebras of few subpowers. In [4] we have proved the Valeriote conjecture for reflexive directed graphs. In [5] we have given equivalent formulations of the Valeriote conjecture. in [6] we have introduced a completely new reduction of CSP problems that allowed the proof of the dichotomy conjecture for various new classes of algebras

The endomorphism semiring of a semilattice

We prove that the endomorphism semiring of a nontrivial semilattice is always subdirectly irreducible and describe its monolith. The endomorphism semiring is congruence simple if and only if the semilattice has both a least and a largest element

Quasiequational Theories of Flat Algebras

We prove that finite flat digraph algebras and, more generally, finite compatible flat algebras satisfying a certain condition are finitely q-based (possess a finite basis for their quasiequations). We also exhibit an example of a twelve-element compatible flat algebra that is not finitely q-based

Radiocommunication test suite for wireless sensor networks

In wireless sensor networks there is a great need for a test environment where multiple network topologies and communication protocols can be easily described, tested and evaluated under different circumstances in a controlled and reproducible way. Such a testbed could reveal the effectiveness or the bottleneck of networks and protocols.Our proposed framework is designed to perform unit tests focusing on the wireless communication by collecting specially designed statistical indices. It supports all WSN platforms, dynamic network topologies, multiple communication modes, Low-Power-Listening, etc.Communication is tied to specific events such as timers, message sending and reception, or control messages. During unit tests, simple messages with unique payloads are transmitted and statistics are collected about the communication in progress. Model verification is also incorporated to ensure data consistency. Since statistics are collected per edge, there is a possibility to analyze the network or a part of it