Connection Matrices and the Definability of Graph Parameters

In this paper we extend and prove in detail the Finite Rank Theorem for connection matrices of graph parameters definable in Monadic Second Order Logic with counting (CMSOL) from B. Godlin, T. Kotek and J.A. Makowsky (2008) and J.A. Makowsky (2009). We demonstrate its vast applicability in simplifying known and new non-definability results of graph properties and finding new non-definability results for graph parameters. We also prove a Feferman-Vaught Theorem for the logic CFOL, First Order Logic with the modular counting quantifiers

Monadic second order finite satisfiability and unbounded tree-width

The finite satisfiability problem of monadic second order logic is decidable only on classes of structures of bounded tree-width by the classic result of Seese (1991). We prove the following problem is decidable: Input: (i) A monadic second order logic sentence $\alpha$, and (ii) a sentence $\beta$ in the two-variable fragment of first order logic extended with counting quantifiers. The vocabularies of $\alpha$ and $\beta$ may intersect. Output: Is there a finite structure which satisfies $\alpha\land\beta$ such that the restriction of the structure to the vocabulary of $\alpha$ has bounded tree-width? (The tree-width of the desired structure is not bounded.) As a consequence, we prove the decidability of the satisfiability problem by a finite structure of bounded tree-width of a logic extending monadic second order logic with linear cardinality constraints of the form $|X_{1}|+\cdots+|X_{r}|<|Y_{1}|+\cdots+|Y_{s}|$, where the $X_{i}$ and $Y_{j}$ are monadic second order variables. We prove the decidability of a similar extension of WS1S

The family house with veterinary attendance

Bakalářská práce řeší novostavbu rodinného domu s provozovnou veterinární ordinace v obci Pstruží. Cílem této práce je vypracovat projektovou dokumentaci pro provedení stavby. Jedná se o samostatně stojící objekt o dvou nadzemních podlažích, který je částečně podsklepený. Prostory, které slouží pro provoz veterinární ordinace, jsou umístěny v suterénu. Dvě nadzemní podlaží jsou určeny pro obývání 4-5 osob.Bachelor´s thesis deals with a new family house with veterinary attendance in the village Pstruží. The aim of this work is to develop design documents for building construction. It is detached building with two floors and basement. Spaces for veterinary medicine are located in the basement. Two floors are intended for occupancy 4-5 persons.

Vanessa Kotek Honors Portfolio

Vanessa Kotek\u27s honors portfolio captured in January 2023