Trees over Infinite Structures and Path Logics with Synchronization

We provide decidability and undecidability results on the model-checking problem for infinite tree structures. These tree structures are built from sequences of elements of infinite relational structures. More precisely, we deal with the tree iteration of a relational structure M in the sense of Shelah-Stupp. In contrast to classical results where model-checking is shown decidable for MSO-logic, we show decidability of the tree model-checking problem for logics that allow only path quantifiers and chain quantifiers (where chains are subsets of paths), as they appear in branching time logics; however, at the same time the tree is enriched by the equal-level relation (which holds between vertices u, v if they are on the same tree level). We separate cleanly the tree logic from the logic used for expressing properties of the underlying structure M. We illustrate the scope of the decidability results by showing that two slight extensions of the framework lead to undecidability. In particular, this applies to the (stronger) tree iteration in the sense of Muchnik-Walukiewicz.Comment: In Proceedings INFINITY 2011, arXiv:1111.267

Approximate MAP Decoding on Tail-Biting Trellises

We propose two approximate algorithms for MAP decoding on tail-biting trellises. The algorithms work on a subset of nodes of the tail-biting trellis, judiciously selected. We report the results of simulations on an AWGN channel using the approximate algorithms on tail-biting trellises for the $(24,12)$ Extended Golay Code and a rate 1/2 convolutional code with memory 6.Comment: 5 pages, 2 figures, ISIT 200

Automated detection and recognition of diagnostically significant ECG changes

The article considers the system of computer analysis of ECG and the software implementation of this system. The system provides for automatic recognition of singular points of ECG and automatic detection of ECG characteristic areas. In the design and implementation of the system there were widely used the finite automata. This allowed to visualize the logic of the system, to avoid design errors and to accelerate the process of creating the system.The analysis of test results developed by the team of the prototype of the computerized ECG analysis system with the advanced capabilities of automated search for characteristic sites allows us to conclude that the reliability of ECG interpretation by a specialist increases with a substantial reduction in the time required to perform this procedure. This positive effect is achieved through the implementation of the procedure for automatic recognition of special ECG points and the use of automated means of searching for ECG lines. The system increases the reliability of decoding ECG by a doctor-cardiologist for the purpose of diagnosis and significantly reduces the time to perform this procedure.Keywords: ECG; ECG annotation; the state machine; state diagram; UML; LabVIE

Vowel Harmony Viewed as Error-Correcting Code

Robustness reduces the risk of information loss. At present the notion of error-correcting codes (ECCs) is used to achieve robustness in technical fields only. Viewing fault-tolerant natural systems as systems equipped with error-correcting codes permits a formal comparison of natural and technical robustness. Instancing natural language (NL), we show differences in technical and natural error-correcting approaches. By picking a specific grammar phenomenon which some NLs exhibit – vowel harmony (VH) – we show that (1) VH can be formalized as an ECC as well as (2) VH adds to the robustness of its NL. We provide empirical as well as formal evidence on this fact. (3) Consequently, the example of VH shows that the notion of an ECC serves as a suitable formal model not only for technical but also for natural robustness