# Linked Coupling Faults Detection by Multirun March Tests
## 2 Linked Coupling Faults  
In the structure of classical models of memory faults, linked faults occupy one of the most prominent places due to the difficulty of their detection using existing march memory tests [3,6,7]. Linked faults are understood as faults of various types, including typical cells involved in several single faults. In the case of linked coupling faults consisting of \(n\) single \(CF_{s}\), \(r<2n\) memory cells are involved. An example of an \(LCF1\) consisting of two \((n=2)\) single coupling faults is illustrated in Figure 2[3]. In this figure, memory cells with addresses \(i<j<k\) are presented sequentially from left to right in the time dependence of their access during the execution of the direct phase of the march test. The designations \(LCF1\) and \(LCF2\) refer to the same \(LCF\) where the manifestation mechanism (scenario) differs and depends on the formation time of the address of the participating cells. As depicted in Figure 2, \(LCF1\) and \(LCF2\) involve \(r=3\) cells and include two single \(CF_{s}\), each consisting of two cells. The above example of \(LCF1\) is presented in numerous literary sources and is positioned as an example of an undetectable fault in the framework of classical march tests [3]. If we assume that the addresses of the cells \(a_{i}\), \(a_{j}\), and \(a_{k}\) are formed in the sequence \(i\), \(j\), and \(k\); that the cells \(a_{i}\) and \(a_{k}\) participate in the fault \(\wedge\)\(<\)\(\uparrow\), \(\downarrow\)\(>\); and that the cells \(a_{j}\) and \(a_{k}\) form a similar fault \(\wedge\)\(<\)\(\uparrow\), \(\downarrow\)\(>\), we have an undetectable fault \(LCF1\). The fact that this fault was not detected refers to one-run march tests using an address sequence satisfying the condition of generating address \(i\) first, then \(j\), and finally \(k\). Then, the successive manifestation of two single faults included in the linked fault \(LCF1\) (Figure 2) leads to a sequential double inversion of the state of the cell \(a_{k}\). Thus, the state of cell \(a_{k}\), when accessed, is always correct, and the \(LCF1\) is undetectable. The considered example of the \(LCF1\) linked fault is given as an argument regarding the nondetection of linked faults in general. However, in particular, the linked fault in Figure 2, consisting of two faults \(\wedge\)\(<\)\(\uparrow\)\(\emptyset\)\(>\) or \(\wedge\)\(<\)\(\uparrow\)\(\downarrow\)\(>\), is detectable. Moreover, when using a one-run march test in which the addresses are generated in the time sequence \(i\), then \(k\), and finally \(j\), the \(LCF1\) designated as \(LCF2\) is detectable regardless of which two CFs form \(LCF2\). Thus, the linked coupling fault, \(LCF\), depends on the number, \(n\), of single linked faults and their varieties and the number, \(r\), of cells participating in the \(LCF\). For the general case, the number of roles and their types, \(A\) and \(V\), for each \(LCF\) cell is also crucial. For example, for the \(LCF1\) where cells \(a_{i}\) and \(a_{j}\) play the aggressor role \(A\), this is the only role  
Figure 2: Linked coupling faults for \(n=2\). for both cells, whereas cell \(a_{k}\) has two victim roles, \(V\). The concept of a role defines the interaction between two cells, so the cell \(a_{k}\) has two roles, \(V\), resulting from the interaction with \(a_{i}\) and \(a_{j}\) within the single \(CF\)s that comprise the \(LCF1\). Abstracting from realistic and unrealistic \(LCF\)s, the sets of which are primarily determined by the design and technological features of the memory, we formulate several statements for the general case of an \(LCF\). First, assuming that \(r\) cells participate in the \(LCF\), we estimate the minimum, \(\min(n)\), and maximum, \(\max(n)\), number, \(n\), of single coupling faults organized in the \(LCF\). Thus, the \(LCF\) consists of single \(CF\)s, and each of the \(r\) cells is included in at least one \(CF\). Statement 1 presents the critical factor for obtaining the boundary values of \(\min(n)\) and \(\max(n)\).