This paper shows that nondeterministic sensing semi-one-way simple k-head finite automata are more powerful than nondeterministic sensing one-way simple k-head finite automata for any k2, and sensing semi-one-way simple 2-head finite automata are more powerful than semi-one-way simple 2-head finite automata, which gives an affirmative answer and a partial solution to two open problems on sensing semi-one-way simple multi-head finite automata in Ref.[3].

This paper investigates a hierarchical property based on the number of inkdots in the accepting powers of sublogarithmic space-bounded multi-inkdot two-way alternating Turing machines with only universal states. For each k1 and any function L(n), let strong-2UTMk(L(n)) (weak-2UTMk(L(n))) be the class of sets accepted by strongly (weakly) L(n) space-bounded k-inkdot two-way alternating Turing machines with only universal states. We show that for each k1, strong-2UTMk+1(log log n) - weak-2UTMk(o(log n)) Ø.

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 two-way alternating Turing machines (2ATM's) with only existential (universal) states which have inkdots and sublogarithmic space. It is shown that for sublogarithmic space-bounded computations, (i) multi-inkdot 2ATM's with only existential states and the ones with only universal states are incomparable, (ii) k-inkdot 2ATM's are better than k-inkdot 2ATM's with only existential (universal) states, k ≥ 0, and (iii) the class of sets accepted by multi-inkdot 2ATM's with only existential (universal) states is not closed under complementation.

We solve open problems about synchronized alternating Turing machines. For example, we show that for any L(n)o(log n), there is a set accepted by a loglog n space bounded two-way synchronized alternating Turing machine with only universal states, but not accepted by any L(n) space bounded one-way synchronized Turing machine with only universal states.

First, we give a method by which any k-valued logic function with n variables can be realized with a cellular array of (k1)kn-1 rows and kn-1 columns. Next, by encoding multi-value to binary one and decoding binary value to multivalue, we give another method by which any k-valued logic function with n variables can be realized with log2k cellular arrays each of which is of kn-1 rows and kn-1 columns.

We introduce alternating multihead finite automata with constant leaf-sizes (AMHFACLs), and investigate several properties of these automata. The main results of this paper are as follows: (1) two-way sensing AMHFACLs can be simulated by two-way nondeterministic simple multihead finite automata, (2) for one-way AMHFACLs, k+1 heads are better than k, and (3) for one-way alternating simple multihead finite automata with constant leaf-sizes, sensing versions are more powerful than non-sensing versions.

This paper investigates the accepting powers of multi-inkdot two-way alternating pushdown automata (Turing machines) with sublogarithmic space and constant leaf-size. For each k1, and each m0, let weak-ASPACEm [L(n),k] denote the class of languages accepted by simultaneously weakly L(n) space-bounded and k leaf-bounded m-inkdot two-way alternating Turing machines, and let strong-2APDAm[L(n),k] denote the class of languages accepted by simultaneously strongly L(n) space-bounded and k leaf-bounded m-inkdot two-way alternating pushdown automata. We show that(1) strong-2APDAm [log log n,k+1]weak-ASPACEm[o(log n),k]φfor each k1 and each m1, and(2) strong-2APDA(m+1) [log log n,k]weak-ASPACEm[o(log n),k]φfor each k1 and each m0.

In [2] Ibarra introduced a restricted version of one-way multihead pushdown automaton (PDA), called a simple one-way multihead PDA, and showed that such machines recognize only languages with semilinear property. The main result of this paper is that for each k 1, simple (sensing) one-way (k + 1)-head PDA's are more powerful than simple (sensing) one-way k-head PDA's. This paper also investigates closure properties for simple (sensing) one-way multihead PDA's

This paper investigates closure properties of one-pebble Turing machines with sublogarithmic space. It shows that for any function log log n L(n) = o(log n), neither of the classes of languages accepted by L(n) space-bounded deterministic and self-verifying nondeterministic one-pebble Turing machines is closed under concatenation, Kleene closure, and length-preserving homomorphism.

This paper investigates some fundamental properties of one-way alternating pushdown automata with sublinear space. We first show that one-way nondeterministic pushdown automata are incomparale with one-way alternating pushdown automata with only universal states, for spaces between log log n and log n, and also for spaces between log n and n/log n. We then show that there exists an infinite space hierarchy among one-way alternating pushdown automata with only universal states which have sublinear space.

This paper gives a hierarchical property on the number of reversals of real-time counter machines. That is, we show that for any k1, a real-time counter machine with 2k+1 reversals is more powerful than one with k reversals.

This paper establishes a relationship among the accepting powers of deterministic, nondeterministic, and alternating one-way auxiliary pushdown automata, for any tape bound below n. Some other related results are also presented.

In this note, we examine several nonclosure properties of the classes of sets (of two-dimensional tapes) accepted by nondeterministic two-dimensional on-line tessellation acceptors, nondeterministic one way parallel sequential array acceptors and deterministic one way parallel sequential array acceptors.

One-way sensing simple multihead finite automata with bounds on the number of times of use of sensing function in accepting computations are studied. It is shown that the languages accepted by one-way sensing simple multihead finite automata with constant sensing function bound satisfy the semilinear property, and that for one-way sensing simple multihead finite automata, m+1 times of the use of sensing function are better than m.

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 the accepting powers of one-way alternating and deterministic multi-counter automata operating in realtime. We partially solve the open problem posed in [4], and show that for each k1, there is a language accepted by a realtime one-way deterministic (k+3)-counter automaton, but not accepted by any realtime one-way alternating k-counter automaton.

Let SeH{0}(k) [NSeH{0}(k)] denote the class of languages over a one-letter alphabet accepted by two-way sensing deterministic [nondeterministic] k-head finite automata. This paper shows that (i) SeH{0}(2)SeH{0}(3), and (ii) NSeH{0}(2) NSeH{0}(3). This gives an affirmative answer to an open problem in Ref. [3].

This paper investigates the accepting powers of one-way alternatiog finite automata with counters and stack-counters (lafacs's) which operate in realtime. (The difference between counter" and stack-counter" is that the latter can be entered without the contents being changed, but the former cannot.) For each k0 and l0 ((k, l)(0, 0)), let 1AFACS(k, l, real) denote the class of sets accepted by realtime one-way alternating finite automata with k counters and l stack-counters, and let 1UFACS(k, l, real) (1NFACS(k, l, real)) denote the class of sets accepted by realtime one-way alternating finite automata with k counters and l stack-counters which have only universal (existential) states. We first investigate a relationship among the accepting powers of realtime lafacs's with only universal states, with only existential states, and with full alternation, and show, for example, that for each k0 and l0 ((k, l)(0, 0)), 1UFACS(k, l, real) 1NFACS(k, l, real) 1AFACS(k, l, real). We then investigate hierarchical properties based on the number of counters and stack-counters, and show, foe example, that for each k0 and l0 ((k, l)(0, 0)), and each X{U, N}, 1XFACS(k1, l, real)1AFACS(k, l, real)φ. We finally investigate a relationship between counters and stack-counters, and show, for example, that for each k0, l0 and m1, and each X{U, N}, 1XFACS(k, lm, real)1AFACS(k2m1, l, real)φ.

This paper investigates a relationship between accepting powers of two-way deterministic one-counter automata and one-pebble off-line deterministic Turing machines operating in space between loglog n and log n, and shows that they are incomparable.