# Linked Coupling Faults Detection by Multirun March Tests
## 3 Necessary and Sufficient Conditions for \(LCF\) Detection
When the aggressor cell cannot fulfill the activation condition, the presence of a faulty memory state (an \(LCF\)) is detected by the wrong state of this cell because tests that detect single \(CFs\) provide the conditions for activating all such faults by setting the required initial state of the aggressor cell \((0,1)\) or performing a transition \((\uparrow,\downarrow)\) in it (see \(CFin\), \(CFid\), and \(CFst\)) [3]. Thus, all \(CF\) aggressor cells included in the \(LCF\) are either the cause of their detection, becoming victims within other \(CFs\), or exercise their influence on the victim cells. In most cases, these tests detect changes in the victim cells relative to the original reference values [3], which follows from the properties of tests that detect the complete set of single coupling faults [3]. The exception is cases of masking that occur when several aggressors influence one cell of the victim. For example, one aggressor changes the reference value of the victim to the opposite, and the second aggressor returns the original value of the victim cell. An example of masking is illustrated in Figure 2 and is described by the formal model \(LCF1\) (4). As observed in this case, cell \(a_{k}\) has two victim roles \(\langle V,V,a_{k}\rangle\) (4), and both are on the same (right) side in the description. When the victim cell has only one victim role (i.e., only one aggressor) before accessing this cell, masking is impossible. If the cell has two victim roles simultaneously, but in both parts of the formal description, the cell content is only read after a single change in its state due to the manifestation of a CF. Accordingly, an _LCF_ is detected. A similar case is illustrated by an example of an _LCF2_ with the formal description of two roles of the victim _LCF3_ of cell \(a_{k}\). However, in this case, one role, \(V\), is on the right, and the second, \(V\), is on the left in the formal description. The masking mechanism is very diverse and is typical for memory devices. However, within the framework, this article considers the case of a memory _LCF_ and the possible masking of the CFs included in them [23]. The guaranteed detection of any fault in the mutual influence of the _CF_, regardless of whether it is included in the linked fault of the _LCF_, is provided by analyzing the state of the victim cell by reading its state after realizing the influence of only one aggressor on it (see Statement 2). An example of the implementation of such a scenario is described by the formal model _LCF3_, where the state of the victim cell \(a_{j}\) (\(\langle V,a_{j},A\rangle\)) is analyzed after only the aggressor cell \(a_{i}\) has been influenced. The presence of at least one cell \(a_{l}\), \(l\in\{i,j,k,\ldots,z\}\) of the formal model _LCF\((a_{i},a_{j},a_{k},\ldots,a_{z})\)_ in the description, where there is only one victim role (on the right or left or both simultaneously), ensures the detection of _LCF\((a_{i},a_{j},a_{k},\ldots,a_{z})\)_, which is a necessary and sufficient condition for _LCF_ detection using a test covering single _CF_s. As demonstrated, the cell role \(B\) in the _LCF_ consists of two roles, each realized in one of the two phases of the test, direct or reverse, which is equivalent to having one role of the victim on the right or left side of the _LCF_ description. The presence of two roles (\(V\) and \(B\)) on the right or left of the description of at least one cell in the _LCF_ also guarantees the detection of this fault because, in one of the phases of the test, the role of \(B\) is equivalent to the role of \(A\). Accordingly, this case is reduced to the case of the presence of one role of the victim. Thus, in the formal model _LCF\((a_{i},a_{j},a_{k},\ldots,a_{z})\)_, corresponding to the scenario of the address sequence of the test, a necessary and sufficient condition for detecting this fault is at least one cell \(a_{l}\) that has only one of the roles of the victim \(V\) or \(B\), or both simultaneously on the right or left.