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Given a text of length n and a pattern of length m, we present a parallel linear algorithm for finding all occurrences of the pattern in the text. The algorithm runs in O(n/p) time using any number of p ⩽ n/log m processors on a concurrent-read concurrent-write parallel random-access-machine.

Alternating Turing machines with restrictions preventing them from returning to a previous configuration model games with rules enforcing such a restriction, for instance, the Chinese version of Go. Such restrictions do not affect the time complexity of problems for alternating Turing machines but space S on a machine with the restriction is equivalent either to time or to space exponential in S on a normal alternating machine, depending on the precise nature of the restriction.

We prove there is no polynomial deterministic space simulation for two-way random-tape probabilistic space (Pr₂SPACE) (as defined in Borodin, A., Cook, S., and Pippenger, N. (1983) Inform. Control 58 113–136) for all functions f: ℕ → ℕ and all α ∈ ℕ, Pr₂SPACE(f(n))DSPACE(f(n)^α). This is the answer to the problem formulated in op cit., whether the deterministic squared-space simulation (for recognizers and transducers) generalizes to the two-way random-tape machine model. We prove, in fact, a stronger result saying that even space-bounded Las Vegas two-way random-tape algorithms (yielding always the correct answer and terminating with probability 1) are exponentially more efficient than the deterministic ones.

We give characterizations of multihead two-way finite automata in terms of multihead reversal-bounded pushdown automata and restricted checking stack automata. In particular, we show that a language is accepted by a 2k-head two-way finite automaton if and only if it is accepted by a k-head two-way pushdown automaton which makes one reversal on its stack. We also show that a 2-head two-way deterministic finite automaton is equivalent to a simple type of two-way deterministic checking stack automaton. This is in contrast to a previously known result which shows that simple two-way nondeterministic checking stack automata are equivalent to nondeterministic linear bounded automata.

Let WRAM [PRAM]be a parallel computer with p processors (RAMs) which share a common memory and are allowed simultaneous reads and writes [only simultaneous reads]. The only type of simultaneous writes allowed is a simultaneous AND: a subset of the processors may write 0 simultaneously into the same memory cell. Let t be the time bound of the computer. We design below families of parallel algorithms that solve the string matching problem with inputs of size n (n is the sum of lengths of the pattern and the text) and have the following performance in terms of p, t and n: (1) For WRAM: pt = O(n) for p ⩽ n/log n (i.e., t ⩾ log n).^† (2) for PRAM: pt = O(n) for p ⩽ n/log² n (i.e., t ⩾ log² n). (3) For WRAM: t = constant for p = n^{1 + ε} and any ε > 0. (4) For WRAM: t = O(log n/log log n) for p = n. Similar families are also obtained for the problem of finding all initial palindromes of a given string.

We prove: (1) every language accepted by a two-way nondeterministic pushdown automaton can be recognized on a random access machine in O(n³/log n) time; (2) every language accepted by a loop-free two-way nondeterministic pushdown automaton can be recognized in O(n³/log² n) time; (3) every context-free language can be recognized on-line in O(n³/log² n) time. We improve the results of Aho, Hopcroft, and Ullman (Inform. Contr. 13, 1968, 186–206), Rytter (Inform. Process. Lett. 16, 1983, 127–129), and Graham, Harrison, and Ruzzo (ACM Trans. Programm. Lang. Systems 2, No. 3, 1980, 415–462).

The expressiveness of branching time tense (temporal) logics whose eventually operators are relativised to general paths into the future is investigated. These logics are interpreted in models obtained by generalising the usual notion of transition system to allow infinite transitions. It is shown that the presence of formulae expressing the future perfect enables one to prove that the expressiveness of the logic can be characterised by a notion of bisimulation on the generalised transition systems. The future perfect is obtained by adding a past tense operator to the language. Finally the power of various tense languages from the literature are investigated in this framework.

We present a data structure based on AVL-trees which allows an insertion or a deletion to be performed in time O(log d), where d is the distance of the position searched for from a finger which points to the end of the file. Moving a finger to a distance d costs O(log d). This result demonstrates the power of the oldest basic data structure, the AVL-tree. A special case of interest is an efficient implementation of searchable priority queues such that Deletemin requires only constant time.

We consider parallel random access machines (PRAM's) with p processors and distributed systems of random access machines (DRAM's) with p processors being partially joint by wires according to a communication graph. For these computational models we prove lower bounds for testing the solvability of linear Diophantine equations and related problems including the knapsack problem. These bounds are achieved by generalizing and simplifying a lower bound for parallel computation trees due to Yao, introducing a new type of computation trees which models computations of DRAM's, and by generalizing a technique used by Paul and Simon and Klein and Meyer auf der Heide to carry over lower bounds from computation trees to RAM's. Thereby we prove that for many problems, p processors cannot speed up a computation by a factor O(p) but only by a factor O(log(p + 1)) and in the case of DRAM's whose communication network has degree c by a factor O(log(c + 1)) only.