A negation-limited circuit is a combinational circuit which includes at most [log(n1)] NOT gates. We show a relationship between the size of negation-limited circuits computing clique functions and the number of NOT gates in the circuits.

We show a relationship between the number of negations in circuits and the size of circuits. More precisely, we construct a Boolean function Hn, and show that there exists an integer t, which can range over only two different values, such that the removal of one NEGATION gate causes an exponential growth of the optimal circuit size for Hn.

In this paper, we show that a parity function with n variables can be computed by a threshold circuit of depth O((log n)/c) and size O((2clog n)/c), for all 1c [log(n+1)]-1. From this construction, we obtain an O(log n/log log n) upper bound for the depth of polylogarithmic size threshold circuits for parity functions. By using the result of Impagliazzo, Paturi and Saks[5], we also show an Ω (log n/log log n) lower bound for the depth of the threshold circuits. This is an answer to the open question posed in [11].

Devanagari is the most widely used script in India. Here, a method is introduced for recognizing Devanagari characters using Neural network. The proposed method reduces the number of output unit necessary for a conventional neural network where the classification is based on a winner take all basis. An automatic coding procedure for representing the output layer of the network and a different method for the final classification is also proposed. Along with the automatic coding procedure, a heuristic method for representing the output units by exploiting the structural information of Devanagari character is also demonstrated. Besides, it has been shown by random representation of the output layer that the representation effects the generalization/performance of the network. The proposed automatic representation gave the recognition rate of 98.09% for 44 categories.

In the filed of cognitive psychology, simple recurrent networks are used for modeling the natural language processing in the human brain. For example, Elman experimentally showed that the simple recurrent networks can predict the right-most word in sentential forms of a particular grammar which can generate compound sentences with high probability. Concerning these results, it is natural to ask whether the computational capability of the simple recurrent networks is sufficient to recognize natural languages. In this paper, we assume that the range of a function computed at each gate of a simple recurrent network is a finite set. This is a quite realistic assumption, because we cannot physically implement a gate whose range is an infinite set. Then, we define equivalence relations between simple recurrent networks and Mealy machines or Moore machines, which are finite automata with output. Then, under our assumption, we show (1) a construction of a Mealy machine which simulates a given simple recurrent network, and (2) a construction of a simple recurrent network which simulates a given Moore machine. From these two constructions, we can conclude that the computational capability of the simple recurrent networks is equal to that of finite automata with output under our assumption.

J. Bresnan and R. M. Kaplan introduced lexical-functional grammars (LFGs, for short) as a new formalism for human language syntax. It is important to show formal properties of this kind of grammars in order to characterize the formal complexity of human languages. In this paper, we will show that the emptiness problem for LFGs is undecidable.

Let S(n) be a space constructible function such that S(n) log n. In this paper, we show that AuxSpTu (S(n),T(n)) NSPACE (S(n)log T(n)), where AuxSpTu (S(n),T(n)) is the class of languages accepted by nondeterministic auxiliary pushdown automata operating simultaneously in O(S(n)) space and O(T(n)) turns of the auxiliary tape head.

We exactly determine the number of negations needed to compute the parity functions and the complement of the parity functions. We show that with k NOT gates, parity can be computed on at most 2k+11 variables, and parity complement on at most 2k+12 variables. The two bounds are shown to be tight.