In this paper we study quantum nondeterminism in multiparty communication. There are three (possibly) different types of nondeterminism in quantum computation: i) strong, ii) weak with classical proofs, and iii) weak with quantum proofs. Here we focus on the first one. A strong quantum nondeterministic protocol accepts a correct input with positive probability and rejects an incorrect input with probability 1. In this work we relate strong quantum nondeterministic multiparty communication complexity to the rank of the communication tensor in the Number-On-Forehead and Number-In-Hand models. In particular, by extending the definition proposed by de Wolf to nondeterministic tensor-rank (nrank), we show that for any boolean function f when there is no prior shared entanglement between the players, 1) in the Number-On-Forehead model the cost is upper-bounded by the logarithm of nrank(f); 2) in the Number-In-Hand model the cost is lower-bounded by the logarithm of nrank(f). Furthermore, we show that when the number of players is o(log log n), we have NQP BQP for Number-On-Forehead communication.

In this paper, the substitutability of the indifferentiability framework with non-sequential scheduling is examined by reformulating the framework through applying the Task-PIOA framework, which provides non-sequential activation with oblivious task sequences. First, the indifferentiability framework with non-sequential scheduling is shown to be able to retain the substitutability. Thus, the substitutability can be applied in another situation that processes of the systems may behave non-sequentially. Next, this framework is shown to be closely related to reducibility of systems. Reducibility is useful to discuss about the construction of a system from a weaker system. Finally, two modelings with respectively sequential scheduling and non-sequential scheduling are shown to be mutually independent. We find examples of systems which are indifferentiable under one model but differentiable under the other. Thus, the importance of scheduling in the indifferentiability framework is clarified.

This paper investigates a relationship between inkdot and one-pebble for two-dimensional finite automata (2-fa's). Especially we show that (1) alternating inkdot 2-fa's are more powerful than nondeterministic one-pebble 2-fa's, and (2) there is a set accepted by an alternating inkdot 2-fa, but not accepted by any alternating one-pebble 2-fa with only universal states.

For each positive integer r 1, a nondeterministic machine M is r path-bounded if for any input word x, there are r computation paths of M on x. This paper investigates the accepting powers of path-bounded one-way (simple) multihead nondeterministic finite automata. It is shown that for each k 2 and r 1, there is a language accepted by an (r + 1) path-bounded one-way nondeterministic k head finite automaton, but not accepted by any r path-bounded one-way nondeterministic k head finite automaton whether or not simple.

This paper investigates the accepting powers of deterministic, Las Vegas, self-verifying nondeterministic, and nondeterministic one-way multi-counter automata with time-bounds. We show that (1) for each k1, there is a language accepted by a Las Vegas one-way k-counter automaton operating in real time, but not accepted by any deterministic one-way k-counter automaton operating in linear time, (2) there is a language accepted by a self-verifying nondeterministic one-way 2-counter automaton operating in real time, but not accepted by any Las Vegas one-way multi-counter automaton operating in polynomial time, (3) there is a language accepted by a self-verifying nondeterministic one-way 1-counter automaton operating in real time, but not accepted by any deterministic one-way multi-counter automaton operating in polynomial time, and (4) there is a language accepted by a nondeterministic one-way 1-counter automaton operating in real time, but not accepted by any self-verifying nondeterministic one-way multi-counter automaton operating in polynomial time.

This paper investigates properties of space-bounded "two-dimensional Turing machines (2-tm's)," whose input tapes are restricted to square ones, with bounded input head reversals in vertical direction. We first investigate a relationship between determinism and nondeterminism for space-bounded and input head reversal-bounded 2-tm's. We then investigate how the number of input head reversals affects the accepting power of sublinearly space-bounded 2-tm's. Finally, we investigate necessary and sufficient spaces for three-way 2-tm's to simulate four-way two-dimensional finite automata with constant input head reversals.

This paper is concerned with a comparative study of the accepting powers of deterministic, Las Vegas, self-verifying nondeterminisic, and nondeterministic (simple) multihead finite automata. We show that (1) for each k 2, one-way deterministic k-head (resp., simple k-head) finite automata are less powerful than one-way Las Vegas k-head (resp., simple k-head) finite automata, (2) there is a language accepted by a one-way self-verifying nondeterministic simple 2-head finite automaton, but not accepted by any one-way deterministic simple multihead finite automaton, (3) there is a language accepted by a one-way nondeterministic 2-head (resp., simple 2-head) finite automaton, but not accepted by any one-way self-verifying nondeterministic multihead (resp., simple multihead) finite automaton, (4) for each k 1, two-way Las Vegas k-head (resp., simple k-head) finite automata have the same accepting powers as two-way self-verifying nondeterministic k-head (resp., simple k-head) finite automata, and (5) two-way Las Vegas simple 2-head finite automata are more powerful than two-way deterministic simple 2-head finite automata.