Jumping Finite Automata and Transducers

Tato bakalářská práce navazuje na studium skákajících konečných automatů a zavádí skákající konečné převodníky. Skákající konečné automaty jsou modifikované konečné automaty tak, že symboly ze vstupní pásky nejsou čteny spojitě zleva-doprava, ale čtecí hlava se může pohybovat po vstupní pásce pomocí skoků. Skákající konečné převodníky jsou podobně modifikované konečné převodníky. Aby bylo možné skákající konečné automaty a převodníky implementovat, byly zavedeny jejich striktně deterministické verze omezením konečné stavové kontroly a modifikací binární skokové relace. Práce se dále zabývá možným využitím skákajících konečných automatů a převodníků a popisem implementace striktně deterministického skákajícího konečného automatu.The bachelor's thesis builds upon the study of jumping finite automata and introduces jumping finite transducers. Jumping finite automata are finite automata modified in such a way that symbols from the input tape are not read continuously from left to right but that the reading head can make moves on the input tape by jumps. Jumping finite transducers are finite transducers modified in a very similar way. In order to implement jumping finite automata and transducers, strictly deterministic versions of them were introduced by restricting the finite state control and by modification of the binary jumping relation. The thesis furthermore focuses on possible usage of jumping finite automata and transducers and on the description of the implementation of strictly deterministic jumping finite automata.

Jumping Finite Automata for Tweet Comprehension

Every day, over one billion social media text messages are generated worldwide, which provides abundant information that can lead to improvements in lives of people through evidence-based decision making. Twitter is rich in such data but there are a number of technical challenges in comprehending tweets including ambiguity of the language used in tweets which is exacerbated in under resourced languages. This paper presents an approach based on Jumping Finite Automata for automatic comprehension of tweets. We construct a WordNet for the language of Kenya (WoLK) based on analysis of tweet structure, formalize the space of tweet variation and abstract the space on a Finite Automata. In addition, we present a software tool called Automata-Aided Tweet Comprehension (ATC) tool that takes raw tweets as input, preprocesses, recognise the syntax and extracts semantic information to 86% success rate

Automata with Nested Pebbles Capture First-Order Logic with Transitive Closure

String languages recognizable in (deterministic) log-space are characterized either by two-way (deterministic) multi-head automata, or following Immerman, by first-order logic with (deterministic) transitive closure. Here we elaborate this result, and match the number of heads to the arity of the transitive closure. More precisely, first-order logic with k-ary deterministic transitive closure has the same power as deterministic automata walking on their input with k heads, additionally using a finite set of nested pebbles. This result is valid for strings, ordered trees, and in general for families of graphs having a fixed automaton that can be used to traverse the nodes of each of the graphs in the family. Other examples of such families are grids, toruses, and rectangular mazes. For nondeterministic automata, the logic is restricted to positive occurrences of transitive closure. The special case of k=1 for trees, shows that single-head deterministic tree-walking automata with nested pebbles are characterized by first-order logic with unary deterministic transitive closure. This refines our earlier result that placed these automata between first-order and monadic second-order logic on trees.Comment: Paper for Logical Methods in Computer Science, 27 pages, 1 figur

Aperiodic tilings and entropy

In this paper we present a construction of Kari-Culik aperiodic tile set - the smallest known until now. With the help of this construction, we prove that this tileset has positive entropy. We also explain why this result was not expected

A Note on a New Class of APCol Systems

We introduce a new acceptance mode for APCol systems (Automaton-like P colonies), variants of P colonies where the environment of the agents is given by a string and during functioning the agents change their own states and process the string similarly to automata. In case of the standard variant, the string is accepted if it can be reduced to the empty word. In this paper, we de ne APCol systems where the agents verify their environment, a model resembling multihead nite automata. In this case, a string of length n is accepted if during every halting computation the length of the environmental string in the con gurations does not change and in the course of the computation every agent applies a rule to a symbol on position i of some of the environmental strings for every i, 1 < i < n at least once. We show that these verifying APCol systems simulate one-way multihead nite automata

Visibly Linear Dynamic Logic

We introduce Visibly Linear Dynamic Logic (VLDL), which extends Linear Temporal Logic (LTL) by temporal operators that are guarded by visibly pushdown languages over finite words. In VLDL one can, e.g., express that a function resets a variable to its original value after its execution, even in the presence of an unbounded number of intermediate recursive calls. We prove that VLDL describes exactly the $\omega$-visibly pushdown languages. Thus it is strictly more expressive than LTL and able to express recursive properties of programs with unbounded call stacks. The main technical contribution of this work is a translation of VLDL into $\omega$-visibly pushdown automata of exponential size via one-way alternating jumping automata. This translation yields exponential-time algorithms for satisfiability, validity, and model checking. We also show that visibly pushdown games with VLDL winning conditions are solvable in triply-exponential time. We prove all these problems to be complete for their respective complexity classes.Comment: 25 Page

Small-world behavior in a system of mobile elements

We analyze the propagation of activity in a system of mobile automata. A number r L^d of elements move as random walkers on a lattice of dimension d, while with a small probability p they can jump to any empty site in the system. We show that this system behaves as a Dynamic Small-World (DSW) and present analytic and numerical results for several quantities. Our analysis shows that the persistence time T* (equivalent to the persistence size L* of small-world networks) scales as T* ~ (r p)^(-t), with t = 1/(d+1).Comment: To appear in Europhysics Letter