SU1410054A1 - Device for determining feasibility matrix of graph - Google Patents

Abstract

The invention relates to the field of computing and can be. used for the study of graphs as well as for the automated solution of information processing problems that allow a theoretical graph representation. The purpose of the invention is to increase the speed by reducing the time for setting the initial information about the topology of the graph. The device contains a matrix of models of arcs 1, a group of elements AND 6, a generator of clock pulses 7, an element of AND 8, an element of HE 9, a decoder 10, a counter 11, a group of elements of AND 4 and a group of delay elements 5, each of the models of arcs 1 consisting of. element I 2, trigger 3 and element I 15. 1 h, n, f-ly, 1 ill. (L about

Description

The invention relates to computing and can be used to study graphs, as well as to automatically solve information processing problems that allow a graph-theoretic representation.

The purpose of the invention is to increase the speed of the device by reducing the time for setting the initial information about the topology of the graph.

The drawing shows a block diagram of the device.

The device contains a matrix of models of arcs 1, each of which consists of the first element AND 2 and trigger 3, the group of elements OR 4, the group of delay elements 5, the group of elements AND 6, the clock pulse generator 7, the element AND 8, the element NOT 9, the decoder 10 , the counter 11, the start-up input 12 of the device, the input of the initial installation 13 of the device, the output 14 of the end of operation of the device, in addition, each model of arc 1 contains the second element I 15.

The device works in the following way.

In the initial state, the start signal 12 has the value O, which blocks the passage of pulses from the generator 7 through the element AND 8 at the output of which is present, blocking the operation of the elements AND 2 models of arcs 1, at the third input of the element 8 and 8

1 from the output of the element HE 9,

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since the counter 11 is reset and on the output of the decoder 10 from 01 to (K + 1) - O

The initial information about the topology of the graph is entered as a matrix adjacent to the triggers of 3 models of arcs 1 through the information inputs of the device, which coincide with the inputs of the initial installation of triggers of 3 models of arcs 1, after which the device is ready for operation. When a signal is applied to the input 12 of the Level 1 start, the pulses from the clock pulse generator 7 through the elements And 8 begin to flow to the counter 1, the state of which is converted by the decoder 10 into a position code. In i, the operation of the device with each clock pulse from the 7 P generator is successively replaced from O to (K + 1), respectively, the position code at the outputs of the decoder 10 is changed. At the same time, at clock cycles P 1. in triggers 3 arc models

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five

l

five

0

1, the row P of the matrix of the intercourse of the given graph is converted into the corresponding rows of the reachability matrix. The transformation takes place in a dim way. At the cycle P M at the output M of the decoder 10, a signal 1 appears, which, through the SHSh 4 element and opened by the clock pulse from the AND 8 element, the AND 6 element enters the inputs of the AND 2 elements of the M row of the matrix of arc models. If in a certain trigger trigger 3. models of arc 1 are recorded 1, then at the output of the corresponding element AND 2 there is a signal 1, meaning that the vertex is reachable from the vertex M. This signal goes through the element OR 4 and And 6 to the inputs of the elements AND Z Corresponding dei rows of the matrix of models of arcs .1, on the outputs of which also appear 1 if there are 1 in the corresponding trigger 3 models of arcs 1, arriving at the inputs of the OR elements .4 with indices that coincide with the indexes of reachable vertices

tires and etc. Thus, on each step P at the outputs of the OR 4 elements corresponding to the vertices reachable from the vertex with index P, signals 1 will be present, which corresponds to row P of the reachability matrix of the graph under study. Information from the outputs of the elements OR 4. It comes through the open elements AND 6 and elements 15 to the information inputs of the triggers 3 of all rows of the matrix of models of arcs 1, but its fixation is performed only in the triggers 3 rows of P, i.e. line number equal to the number of the current measure. Fixation is provided by applying to the second inputs of the AND 15 element a signal for entering information into the triggers of the 3 P th lines of the matrix of models of arcs 1. From the P output of the decoder 10 delayed by the corresponding delay element 5 on the leading edge for the time needed to form rows of reachability matrix in groups of elements OR 4 and elements AND 6 .. After recording the row P of the matrix of reachability, the clock signal from the output of element AND 8 takes the value O, which ensures a short-term blocking of elements AND 6 and zeroing the outputs of all elements And 2 models of arcs 1, as well as the outputs of the elements OR 4, This provides an exception

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nor feedbacks, having place in the presence of strongly connected components in the graph, on the reliability of the information in the formed reachability matrix. The next clock pulse from generator 7 transfers the counter 1 to the P + 1 state and the device generates the next row of the reachability matrix, and so on. until reaching the state K + 1, when the triggers of the .3 models of arcs 1 completely form a matrix of reachability, while at the output of the (K + 1) th decoder 10 there appears 1 blocking the HE 9 element and the AND 8 element passing pulses from generator 7, which blocks the operation of the device as a whole. The presence of 1 at the (K + 1) th output of the decoder 10 also serves as the signal for finishing operation 14, by which the signal 12 is started from the device inputs and the initial setting signal 13 is output, while the counter 11 is nullified and after being triggered by 3 models arcs 1. initial information about the topology of the next graph under study, the device is ready for a new work cycle.

Claims (2)

1. A device for determining a reachability matrix of a graph, containing a clock pulse generator, an element AND, an element NOT, a group of elements AND, a matrix of models of arcs, a decoder, a counter, whose information outputs are connected to the information inputs of the decoder, (K + 1), and whose output (where K is the number of vertices in the graph) is connected to the input of the NOT element, the output of the clock generator is connected to the first input of the AND element, the second input of which is the input of the device, which is increase the speed of the device by reducing the task time t. initial information about the topology of the graph, the group of elements OR is entered into it, the group of elements of the delay, the output of the element is NOT connected to the third input of the AND element whose output is connected to the first inputs of the AND elements of the group and to the counter input of the counter whose reset input is the reset input device, the M-th output of the decoder (where M 1, ..., K) is connected to the first input of the corresponding M-th element of the 1SH group and to the input of the corresponding M-th delay element of the group, the output of which is connected to the first inputs of the models of arcs M- th row of the matrix, to The main input from the second (K + 1) -th and M-th element of the OR group is connected to the output of the corresponding arc model of the M-th column of the matrix, and the M-th element of the OR group (where M 1, ..., K) is connected to the second entrance of the Mth element And groups The inputs of the arcs of the M-th matrix of the matrix and with the third inputs of the models of the arcs of the M-th row of the matrix, (K + 1) -th output of the decoder is the output of the sign of the end of the device. 2. The device according to A.1, about tl and - that each model of the arc contains the first and second elements And the trigger, the output of which is connected to the first input of the first element And, and the input of the installation in 1 is connected to the output of the second element And The first and second inputs of which are respectively the first and second inputs of the arc model, the second input of the first AND element, is the third input of the arc model, and the output of the AND element is the output of the model arc.