# Linked Coupling Faults Detection by Multirun March Tests
## 3 Necessary and Sufficient Conditions for \(LCF\) Detection
For example, from the description of \(LCF1\), it follows that this linked fault is formed from two single \(CFs\): \(CF(a_{i},a_{k})=\langle a_{i},A\rangle\), \(\langle V,a_{k}\rangle\) and \(CF(a_{j},a_{k})=\langle a_{j},A\rangle\),\(\langle V,a_{k}\rangle\). The ordered access to the cells \(a_{i},a_{j},a_{k},\ldots,a_{z}\) of the fault \(LCF(a_{i},a_{j},a_{k},\ldots,a_{z})\), when implementing the march test element, is determined by the time sequence of generating their addresses \(i,j,k,\ldots,z\). This sequence is a crucial element of the formal description of the \(LCF\), which, for example, can be observed from the descriptions (4) of the \(LCF\) in Figure 2. Indeed, for the sequence of addresses \(i,j\), and \(k\), we have the \(LCF1\) description of the fault, and for \(i,k\), and \(j\), another description is used: \(LCF2\) (4). The position of a particular cell (e.g., cell \(a_{k}\) in its description) and the description itself in the formal \(LCF\) model correspond to the temporal order of accessing this cell when implementing the march test element. For example, in the formal model \(LCF1=\{\langle a_{i},-A\rangle;\langle-,a_{j},A\rangle;\langle V,V,a_{k} \rangle\}\), the description of cell \(a_{k}\) is in the third position because the test generates the address \(k\) after forming addresses \(i\) and \(j\). In the description of \(\langle V,V,a_{k}\rangle\) of cell \(a_{k}\), its designation is also given in the third position. Thus, the basis of the new formal \(LCF\) model is the three roles that the cells of the linked coupling fault perform, aggressor (\(A\)), victim (\(V\)), and both (\(B\)), performed by two cells simultaneously in relation to each other. In reality, the proposed model describes the scenario for implementing the roles of memory fault cells, determined by the march test and the address sequence in this test to access the cells. For tests with a maximum fault coverage \(CF\), the scenario is specified only by the address sequence, displayed in the formal \(LCF\) model, as demonstrated in the examples of \(LCF1\) and \(LCF2\). For each cell \(a_{i},a_{j},a_{k},\ldots,a_{z}\), the \(LCFs\) distinguish between the left and right in the description. Moreover, those fault cells activated before activating the current cell are on the left side and are on the right side after activation. Activation refers to accessing a memory cell under the march element of the test and performing the corresponding write and read operations. The formal \(LCF\) model allows us to formulate the conditions for detecting such faults using one-run march tests. **Statement 2**. : _The necessary and sufficient conditions for detecting a linked coupling fault \(\operatorname{LCF}(a_{i},a_{j},a_{k},\ldots,a_{z})\) are listed below._  
1. _The application of a march test with an arbitrary address sequence, which detects all kinds of single coupling faults._
2. _The presence in the formal model_ \(\operatorname{LCF}(a_{i},a_{j},a_{k},\ldots,a_{z})\) _of a fault that corresponds to the address sequence of the applied test, at least one cell_ \(a_{l}\)_,_ \(l\in\{i,j,k,\ldots,z\}\)_, where only one role V is present in the right, or on the left side of the description, or in both parts._  
As demonstrated, an arbitrary fault \(LCF(a_{i},a_{j},a_{k},\ldots,a_{z})\) is a composition of single CFs, where the entire set is detected by march tests, for example, the March LA and March LR[13; 14]. All possible single \(CFs\) are guaranteed to be detected by the indicated tests only if they are not included in the \(LCF\) fault. When single \(CFs\) are included in the \(LCF\), these tests detect them either by the wrong state of the aggressor cell or are guaranteed to provide a condition for their activation by changing the state of the victim cell and detecting the wrong state.