Let G be a 2-edge-connected graph with o vertices of odd degree. It is well-known that one should (and can) add o 2 edges to G in order to obtain a graph which admits a nowhere-zero 2-flow. We prove that one can add to G a set of ≤ b o 4c, d2b o 5ce, and d2b o 7ce edges such that the resulting graph admits a nowhere-zero 3-flow, 4-flow, and 5-flow, respectively.

Validation of VHDL descriptions at the early phases of the microelectronic design is one of the most time consuming task design. This paper presents a test vector generation method for behavioral VHDL design. This method analyzes control and dependence flow of VHDL program. We use the cyclomatic complexity, that is a software metric based on a graph associated with the control part of software:...

Formal Specification languages are being widely used for system specification and testing. Highly critical systems such as real time systems, avionics, and medical systems are represented using Formal specification languages. Formal specifications based testing is mostly performed using black box testing approaches thus testing only the set of inputs and outputs of the system. The formal specif...

We show that every bridgeless cubic graph without a Petersen minor has a nowhere-zero 5-flow. This approximates the known 4-flow conjecture of Tutte. A graph has a nowhere-zero k-flow if its edges can be oriented and assigned nonzero elements of the group Zk so that the sum of the incoming values equals the sum of the outcoming ones for every vertex of the graph. An equivalent definition we get...

We categorize and compare diierent representations of program dependence graphs, including the Control Flow Graph (CFG) which is a sequential representation lacking data dependences, the Program Dependence Graph (PDG) which is a parallel representation of a sequential program and is comprised of control and data dependences, and more generally, the Parallel Program Graph (PPG) which is a parall...

We are using ML to build a compiler that does low-level optimization. To support optimizations in classic imperative style, we built a control-flow graph using mutable pointers and other mutable state in the nodes. This decision proved unfortunate: the mutable flow graph was big and complex, and it led to many bugs. We have replaced it by a smaller, simpler, applicative flow graph based on Huet...

Power flow analyses are essential for the correct operation of power grids, however, electricity systems becoming increasingly complex to analyze with conventional numerical methods. The present work proposes a typed graph neural network based approach solve problem. networks trained on benchmark grid cases which modified by varying injections (load and generation), branch characteristics topol...