Parameterizing cut sets in a graph by the number of their components

For a connected graph G=(V,E), a subset U⊆V is a disconnected cut if U disconnects G and the subgraph G[U] induced by U is disconnected as well. A cut U is a k-cut if G[U] contains exactly k(≥1) components. More specifically, a k-cut U is a (k,?)-cut if V?U induces a subgraph with exactly ?(≥2) components. The Disconnected Cut problem is to test whether a graph has a disconnected cut and is known to be NP-complete. The problems k-Cut and (k,?)-Cut are to test whether a graph has a k-cut or (k,?)-cut, respectively. By pinpointing a close relationship to graph contractibility problems we show that (k,?)-Cut is in P for k=1 and any fixed constant ?≥2, while it is NP-complete for any fixed pair k,?≥2. We then prove that k-Cut is in P for k=1 and NP-complete for any fixed k≥2. On the other hand, for every fixed integer g≥0, we present an FPT algorithm that solves (k,?)-Cut on graphs of Euler genus at most g when parameterized by k+?. By modifying this algorithm we can also show that k-Cut is in FPT for this graph class when parameterized by k. Finally, we show that Disconnected Cut is solvable in polynomial time for minor-closed classes of graphs excluding some apex graph.     

Editorial

Higher-Order and Symbolic Computation -     

Codevelopmental learning between human and humanoid robot using a dynamic neural-network model.

This paper examines characteristics of interactive learning between human tutors and a robot having a dynamic neural-network model, which is inspired by human parietal cortex functions. A humanoid robot, with a recurrent neural network that has a hierarchical structure, learns to manipulate objects. Robots learn tasks in repeated self-trials with the assistance of human interaction, which provides physical guidance until the tasks are mastered and learning is consolidated within the neural networks. Experimental results and the analyses showed the following: 1) codevelopmental shaping of task behaviors stems from interactions between the robot and a tutor; 2) dynamic structures for articulating and sequencing of behavior primitives are self-organized in the hierarchically organized network; and 3) such structures can afford both generalization and context dependency in generating skilled behaviors.     

Bottom-up pyramid cellular acceptors with three-dimensional layers

In 1997, C.R. Dyer and A. Rosenfeld introduced an acceptor on a two-dimensional pattern (or tape), called the pyramid cellular acceptor, and demonstrated that many useful recognition tasks are executed by pyramid cellular acceptors in time proportional to the logarithm of the diameter of the input. They also introduced a bottom-up pyramid cellular acceptor which is a restricted version of the pyramid cellular acceptor, and proposed some interesting open problems of the bottom-up pyramid cellular acceptors. On the other hand, we think that the study of threedimensional automata has been meaningful as the computational model of three-dimensional information processing such as computer vision, robotics, and so forth. In this paper, we investigate about bottom-up pyramid cellular acceptors with three-dimensional layers, and show their some accepting powers. This work was presented in part at the 13th International Symposium on Artificial Life and Robotics, Oita, Japan, January 31–February 2, 2008     

Translational lemmas for DLOGTIME-uniform circuits,alternating TMs,and PRAMs

We present translational lemmas for the three standard models of parallel computation, and apply them to obtain tight hierarchy results. It is shown that, for arbitrarily small rational constant , (i) there is a language which can be accepted by a -uniform circuit family of depth and size but not by any -uniform circuit family of depth and size , (ii) there is a language which can be accepted by a -time -space ATM with l worktapes but not by any -time -space ATM with the same l worktapes if the number of tape symbols is fixed, and (iii) there is a language which can be accepted by a -time PRAM with processors but not by any -time PRAM with processors. Here, c > 0, d ≥ 1, r ₁ > 1, and r ₂ ≥ 1 are arbitrary rational constants, and l ≥ 2 is an arbitrary integer. Preliminary versions of different parts of this paper appeared in Proc. MCU 2004 (LNCS 3354) and Proc. FCT 2005 (LNCS 3623).     

Making Java work for microcontroller applications

The authors investigate complete system development using a Java machine aimed at FPGA devices. A new design strategy targets a single FPGA chip, within which the dedicated Java microcontroller-FemtoJava-is synthesized     

Minimum cost source location problem with vertex-connectivity requirements in digraphs

Given a digraph (or an undirected graph) G=(V,E) with a set V of vertices v with nonnegative real costs w(v), and a set E of edges and a positive integer k, we deal with the problem of finding a minimum cost subset SV such that, for each vertex vV−S, there are k vertex-disjoint paths from S to v. In this paper, we show that the problem can be solved by a greedy algorithm in time in a digraph (or in time in an undirected graph), where n=|V| and m=|E|. Based on this, given a digraph and two integers k and ℓ, we also give a polynomial time algorithm for finding a minimum cost subset SV such that for each vertex vV−S, there are k vertex-disjoint paths from S to v as well as ℓ vertex-disjoint paths from v to S.     

Group weighted finite transducers

We consider weighted finite transducers over arbitrary groups, that is finite transducers having a counter in which, at any step, a value of the group is stored but no information regarding the content of this counter is available until the computation is finished. The computation is valid if the counter value is the neutral element of the group. We generalize here some results from [8] and [17]. Received: 28 January 2001 / 5 June 2001     

Case learning for CBR-based collision avoidance systems

With the rapid development of case-based reasoning (CBR) techniques, CBR has been widely applied to real-world applications such as collision avoidance systems. A successful CBR-based system relies on a high-quality case base, and a case creation technique for generating such a case base is highly required. In this paper, we propose an automated case learning method for CBR-based collision avoidance systems. Building on techniques from CBR and natural language processing, we developed a methodology for learning cases from maritime affair records. After giving an overview on the developed systems, we present the methodology and the experiments conducted in case creation and case evaluation. The experimental results demonstrated the usefulness and applicability of the case learning approach for generating cases from the historic maritime affair records.