Turing Machines on Graphs and Inescapable Groups

Some improvements in fuzzy turing machines

In this paper, we improve some previous definitions of fuzzy-type Turing machines to obtain degrees of accepting and rejecting in a computational manner. We apply a BFS-based search method and some level’s upper bounds to propose a computational process in calculating degrees of accepting and rejecting. Next, we introduce the class of Extended Fuzzy Turing Machines equipped with indeterminacy s...

On Extremal Graph Theory, Explicit Algebraic Constructions of Extremal Graphs and Corresponding Turing Encryption Machines

We observe recent results on the applications of extremal graph theory to cryptography. Classical Extremal Graph Theory contains Erdős Even Circuite Theorem and other remarkable results on the maximal size of graphs without certain cycles. Finite automaton is roughly a directed graph with labels on directed arrows. The most important advantage of Turing machine in comparison with finite automat...

On Separators, Segregators and Time versus Space

We give the first extension of the result due to Paul, Pippenger, Szemeredi and Trotter [24] that deterministic linear time is distinct from nondeterministic linear time. We show that NTIME(n √ log∗(n)) 6= DTIME(n √ log∗(n)). We show that if the class of multi-pushdown graphs has (o(n), o(n/log(n))) segregators, then NTIME(nlog(n)) 6= DTIME(nlog(n)). We also show that atleast one of the followi...

On the Transition Graphs of Turing Machines

Power of Nondetreministic JAGs on Cayley graphs

The Immerman-Szelepcsenyi Theorem uses an algorithm for co-stconnectivity based on inductive counting to prove that NLOGSPACE is closed under complementation. We want to investigate whether counting is necessary for this theorem to hold. Concretely, we show that Nondeterministic Jumping Graph Autmata (ND-JAGs) (pebble automata on graphs), on several families of Cayley graphs, are equal in power...