Spring 2017 CIS 262 Automata , Computability and Complexity
نویسنده
چکیده
Problem B1 (40 pts). Give a context-free grammar for the language over the alphabet {a, b, c} given by L = {xcy | x 6= y, x, y ∈ {a, b}∗}. Hint . At first glance, this seems impossible. Think nondeterministically. You need to figure out how to express that x 6= y in such a way that you can write grammar rules that enforce this condition. Obviously, this is the case if |x| < |y| or |y| < |x|. Another possibility is that x and y differ by some symbol in the same position (scanning from left ro right). If you do it “right,” you choice of productions should yield a justification of the correctness of your grammar.
منابع مشابه
Reduction of Computational Complexity in Finite State Automata Explosion of Networked System Diagnosis (RESEARCH NOTE)
This research puts forward rough finite state automata which have been represented by two variants of BDD called ROBDD and ZBDD. The proposed structures have been used in networked system diagnosis and can overcome cominatorial explosion. In implementation the CUDD - Colorado University Decision Diagrams package is used. A mathematical proof for claimed complexity are provided which shows ZBDD ...
متن کاملPlanarity of Knots, Register Automata and LogSpace Computability
In this paper we investigate the complexity of planarity of knot diagrams encoded by Gauss words, both in terms of recognition by automata over infinite alphabets and in terms of classical logarithmic space complexity. As the main result, we show that recognition of planarity of unsigned Gauss words can be done in deterministic logarithmic space and by deterministic register automata. We also d...
متن کاملDecidability and Complexity Results for Timed Automata and Semi-linear Hybrid Automata
We define a new class of hybrid automata for which reachability is decidable—a proper superclass of the initialized rectangular hybrid automata—by taking parallel compositions of simple components. Attempting to generalize, we encounter timed automata with algebraic constants. We show that reachability is undecidable for these algebraic timed automata by simulating two-counter Minsky machines. ...
متن کاملOn the computability of graph Turing machines
We consider graph Turing machines, a model of parallel computation on a graph, in which each vertex is only capable of performing one of a finite number of operations. This model of computation is a natural generalization of several well-studied notions of computation, including ordinary Turing machines, cellular automata, and parallel graph dynamical systems. We analyze the power of computatio...
متن کاملFull characterization of attractors for two intersected asynchronous Boolean automata cycles
Nowadays, the understanding of Boolean automata networks dynamics takes an important place in various domains of computer science such as computability, complexity and discrete dynamical systems. Basing ourselves on these specific mathematical objects, in this paper, we make a step further in this understanding by focusing on their cycles, whose necessity in networks is known as the brick of th...
متن کامل