This paper first investigates a relationship between inkdot-depth and inkdot-size of inkdot two-way alternating Turing machines and pushdown automata with sublogarithmic space, and shows that there exists a language accepted by a strongly loglog n space-bounded alternating pushdown automaton with inkdot-depth 1, but not accepted by any weakly o (log n) space-bounded and d (n) inkdot-size bounded alternating Turing machine, for any function d (n) such that limn [d (n)log n/n1/2] = 0. In this paper, we also show that there exists an infinite space hierarchy among two-way alternating pushdown automata with sublogarithmic space.

This paper investigates some fundamental properties of alternating one-way (or two-way) pushdown automata (pda's) with sublogarithmic space. We first show that strongly (weakly) sublogarithmic space-bounded two-way alternating pda's are more powerful than one-way alternating pda's with the same space-bound. Then, we show that weakly sublogarithmic space-bounded two-way (one-way) alternating pda's are more powerful than two-way (one-way) nondeterministic pda's and alternating pda's with only universal states using the same space, and we also show that weakly sublogarithmic space-bounded one-way nondeterministic Turing machines are incomparable with one-way alternating Turing machines with only universal states using the same space. Furthermore, we investigate several fundamental closure properties, and show that the class of languages accepted by weakly sublogarithmic space-bounded one-way alternating pda's and the class of languages accepted by sublogarithmic space-bounded two-way deterministic pda's (nondeterministic pda's, alternating pda's with only universal states) are not closed under concatenation, Kleene closure, and length preserving homomorphism. Finally, we briefly investigate a relationship between 'strongly' and 'weakly'.

It was unknown whether there exists a language accepted by a two-way nondeterministic one counter automaton, but not accepted by any nondeterministic rebound automaton. This paper solves this problem, and shows that there exists such a language.

Inoue et al. introduced an automaton on a two-dimensional tape, which decides acceptance or rejection of an input tape by scanning the tape from various sides by various automata which move one way, and investigated the accepting power of such an automaton. This paper continues the investigation of this type of automata, especially, -type automata (obtained by combining four three-way two-dimensional deterministic finite automata (tr2-dfa's) in "or" fashion) and -type automata (obtained by combining four tr2-dfa's in "and" fashion). We first investigate a relationship between the accepting powers of -type automata and -type automata, and show that they are incomparable. Then, we investigate a hierarchy of the accepting powers based on the number of tr2-dfa's combined. Finally, we briefly describe a relationship between the accepting powers of automata obtained by combining three-way two-dimensional deterministic and nondeterministic finite automata.

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.

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.

Let [AONTM(L(n))] ([AOFFTM(L(n))]) be the class of sets accepted by L(n) space bounded alternating on-line (off-line) Turing machines. This paper first gives another proof of the fact that [AONTM(L(n))][AOFFTM(L(n))] for any L(n) such that L(n) log log n and limnL(n)/log n=0. We then show that there exists an infinite hierarchy among [AONTM(L(n))]'s and L[AOFFTM(L(n))]'s with log log nL(n)log n. Finally, we show that [AONTM(L(n))] is not closed under concatenation, Kleene closure, and length preserving homomorphism for any L(n)log log n and limnL(n)/log n=0.

The hierarchies of multihead finite automata over a one-letter alphabet are investigated. Let SeH(k) [NSeH(k) ] denote the class of languages over a one-letter alphabet accepted by deterministic [nondeterministic] sensing two-way k-head finite automata. Let H (k)s[NH(k)s] denote the class of sets of square tapes over a one-letter alphabet accepted by two-dimensional four-way deterministic [nondeterministic] k-head finite automata. Let SeH(k)s[NSeH(k)s] denote the class of sets of square tapes over a one-letter alphabet accepted by two-dimensional four-way sensing deterministic [nondeterministic] k-head finite automata. This paper shows that SeH(k) SeH(k1) and NSeH(k) NSeH(k1) hold for all k3. It is also shown that H(k)s[NH(k)s] H(k1)s[NH (k1)s] and SeH (k)s[NSeH(k)s] SeH(k1)s[NSeH(k1)s] hold for all k1.

For each two positive integers r, s, let [1DCM(r)-Time(ns)] ([1NCM(r)-Time(ns)]) and [1DCM(r)-Space(ns)] ([1NCM(r)-Space(ns)]) be the classes of languages accepted in time ns and in space ns, respectively, by one-way deterministic (nondeterministic) r-counter machines. We show that for each X{D, N}, [1XCM(r)-Time(ns)][1XCM(r+1)-Time(ns)] and [1XCM(r)-Space(ns)][1XCM(r+1)-Space(ns)]. We also investigate the relationships between one-way multicounter machines and cooperating systems of one-way finite automata. In particular, it is shown that one-way (one-) counter machines and cooperating systems of two one-way finite automata are equivalent in accepting power.

This paper investigates the accepting powers of one-way alternating multi-stack-counter automata (lamsca's) and one-way alternating multi-counter automata (lamsca's) which operate in realtime. For each k1, let 1ASCA (k, real) (1ACA(k, real)) denote the class of sets accepted by realtime one-way alternating k-stach-counter (k-counter) automata, and let 1USCA(k, real)(1UCA(k, real)) denote the class of sets accepted by realtime one-way alternating k-stack-counter (k-counter) automata with only universal states. We first investigate a relationship between the accepting powers of realtime lamsca's (lamca's) with only universal states, with only existential states, and with full alternation. We then investigate hierarchical properties based on the numbers of counters and stackcounters, and show, for example, that for each k1, 1USCA(k+1, real)-1ASCA(k, real)φ and 1UCA(k+1, real)-1ACA(k, real)φ. We finally investigate a relationship between the accepting powers of realtime lamsca's and lamca's, and show, for example, that there are no i and j such that 1UCA(i, real)=1USCA(j, real), and 1USCA(k, real)-1ACA(k, real)φ for each k1.

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 introduces a 1-inkdot two-way alternating pushdown automaton which is a two-way alternating pushdown automaton (2apda) with the additional power of marking at most 1 tape-cell on the input (with an inkdot) once. We first investigate a relationship between the accepting powers of sublogarithmically space-bounded 2apda's with and without 1 inkdot, and show, for example, that sublogarithmically space-bounded 2apda's with 1 inkdot are more powerful than those which have no inkdots. We next investigate an alternation hierarchy for sublogarithmically space-bounded 1-inkdot 2apda's, and show that the alternation hierarchy on the first level for 1-inkdot 2apda's holds, and we also show that 1-inkdot two-way nondeterministic pushdown automata using sublogarithmic space are incomparable with 1-inkdot two-way alternating pushdown automata with only universal states using the same space.

This paper introduces a new class of machines called multihead marker finite automata, and investigates how the number of markers affects its accepting power. Let HM{0}(i, j)(NHM{0}(i, j))denote the class of languages over a one-letter alphabet accepted by two-way deterministic (nondeterminstic) i-head finite automata with j markers. We show that HM{0} (i, j) HM{0}(i, j1) and NHM{0}(i, j) NHM{0}(i, j+1) for each i2, j0.

This paper introduces an alternating rebound Turing machine and investigates some fundamental properties of it. Let DRTM (NRTM,ARTM) denote a deterministic (nondeterministic and alternating) rebound Turing machine, and URTM denote an ARTM with only universal states. We first investigate a relationship between the accepting powers of rebound machines and ordinary machines, and show, for example, that (1) there exists a language accepted by a deterministic rebound automaton, but not accepted by any o(log n) space-bounded alternating Turing machine, (2) alternating rebound automata are equivalent to two-way alternating counter automata, and (3) deterministic rebound counter automata are more powerful than two-way deterministic counter automata. We next investigate a relationship among the accepting powers of DRTM's, NRTM's, URTM's and ARTM's, and show that there exists a language accepted by alternating rebound automata, but not accepted by any o(logn) space-bounded NRTM (URTM). Then we show that there exists an infinite space hierarchy for DRTM's (NRTM's, URTM's) with spaces below log n. Furthermore, we investigate a relationship between the strong and weak modes of space complexity, and finally show that the classes of languages accepted by o(logn) space-bounded DRTM's (NRTM's, URTM's) are not closed under concatenation and Kleene .

This paper investigates some fundamental properties of 2-way alternating multi-counter automata (2amca's) with only existential (universal) states which have sublinear space and 1 inkdot. It is shown that for any function s(n) log n such that log s(n)=o(log n), s(n) space-bounded 1-inkdot 2amca's with only existential states are incomparable with the ones with only universal states, and the ones with only existential (universal) states are not closed under complementation.

The main purpose of this paper is to show that, for any L(n) such that L(n)logn and [L(n)/n]0, L(n) space bounded alternating on-line Turing machines with only universal states are less powerful than ordinary L(n) space bounded alternating on-line Turing machines. Closure properties are also discussed.

This paper investigates the properties of synchronized alternating one-way multicounter machines (lsamcm's) which operate in real time (lsamcm-real's) and whose leaf-sizes are bounded by a constant or some function of the length of an input. Leaf-size reflects the number of processors which run in parallel in scanning a given input. We first consider the hieracrchies of lsamcm-real's based on the number of counters and constant leaf-sizes. We next show that lsamcm-real's are less powerful than lsamcm's which operate in linear time when the leaf-sizes of these machines are bounded by a function L(n) such that limn[L(n) log n/n]0 and L(n)2.

There have been several interesting investigations on the space functions constructed by one-dimensional or two-dimensional Turing machines. On the other hand, as far as we know, there is no investigation about the space functions constructed by three-dimensional Turing machines. In this paper, we investigate about space constructibility by three-dimensional deterministic Turing machines with cubic inputs, and show that the functions log*n and log(k)n, k1, are fully space constructible by these machines.

It has already been known that there exists an infinite hierarchy of the classes of sets of square tapes accepted by deterministic space-bounded two-dimensional Turing machines with spaces below log m. This paper shows that there exists an infinite hierarchy of the classes of sets of square tapes accepted by nondeterministic space-bounded two-dimensional Turing machines with spaces less than or equal to log m.

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].