Inadmissible Class of Boolean Functions under Stuck-at Faults

Many underlying structural and functional factors that determine the fault behavior of a combinational network, are not yet fully understood. In this paper, we show that there exists a large class of Boolean functions, called root functions, which can never appear as faulty response in irredundant two-level circuits even when any arbitrary multiple stuck-at faults are injected. Conversely, we show that any other Boolean function can appear as a faulty response from an irredundant realization of some root function under certain stuck-at faults. We characterize this new class of functions and show that for n variables, their number is exactly equal to the number of independent dominating sets (Harary and Livingston, Appl. Math. Lett., 1993) in a Boolean n-cube. We report some bounds and enumerate the total number of root functions up to 6 variables. Finally, we point out several open problems and possible applications of root functions in logic design and testing

Symmetry Breaking for Answer Set Programming

In the context of answer set programming, this work investigates symmetry detection and symmetry breaking to eliminate symmetric parts of the search space and, thereby, simplify the solution process. We contribute a reduction of symmetry detection to a graph automorphism problem which allows to extract symmetries of a logic program from the symmetries of the constructed coloured graph. We also propose an encoding of symmetry-breaking constraints in terms of permutation cycles and use only generators in this process which implicitly represent symmetries and always with exponential compression. These ideas are formulated as preprocessing and implemented in a completely automated flow that first detects symmetries from a given answer set program, adds symmetry-breaking constraints, and can be applied to any existing answer set solver. We demonstrate computational impact on benchmarks versus direct application of the solver. Furthermore, we explore symmetry breaking for answer set programming in two domains: first, constraint answer set programming as a novel approach to represent and solve constraint satisfaction problems, and second, distributed nonmonotonic multi-context systems. In particular, we formulate a translation-based approach to constraint answer set solving which allows for the application of our symmetry detection and symmetry breaking methods. To compare their performance with a-priori symmetry breaking techniques, we also contribute a decomposition of the global value precedence constraint that enforces domain consistency on the original constraint via the unit-propagation of an answer set solver. We evaluate both options in an empirical analysis. In the context of distributed nonmonotonic multi-context system, we develop an algorithm for distributed symmetry detection and also carry over symmetry-breaking constraints for distributed answer set programming.Comment: Diploma thesis. Vienna University of Technology, August 201

Constraint satisfaction problems in clausal form

This is the report-version of a mini-series of two articles on the foundations of satisfiability of conjunctive normal forms with non-boolean variables, to appear in Fundamenta Informaticae, 2011. These two parts are here bundled in one report, each part yielding a chapter. Generalised conjunctive normal forms are considered, allowing literals of the form "variable not-equal value". The first part sets the foundations for the theory of autarkies, with emphasise on matching autarkies. Main results concern various polynomial time results in dependency on the deficiency. The second part considers translations to boolean clause-sets and irredundancy as well as minimal unsatisfiability. Main results concern classification of minimally unsatisfiable clause-sets and the relations to the hermitian rank of graphs. Both parts contain also discussions of many open problems.Comment: 91 pages, to appear in Fundamenta Informaticae, 2011, as Constraint satisfaction problems in clausal form I: Autarkies and deficiency, Constraint satisfaction problems in clausal form II: Minimal unsatisfiability and conflict structur

Minimal test set for stuck-at faults in VLSI

Minimal test sets have the property that each input vector simultaneously tests several faults in a network. Existing techniques to determine a minimal set of detection tests rely heavily on complicated algebraic techniques. In this paper, two new methods are presented which do not require Boolean algebra or Karnaugh maps. The first is a graphical approach using fault folding graphs. The second is a design by inspection technique. This work follows the unique approach of first finding all the faults that can be detected by a single test. This tremendously reduces the work required to determine a minimal test set. The design by inspection method could be automated for programmatic generation of minimal stuck-at fault tests

Processing and Transmission of Information

Contains reports on seven research projects.Lincoln Laboratory (Purchase Order DDL-B222

Custom Integrated Circuits

Contains reports on twelve research projects.Analog Devices, Inc.International Business Machines, Inc.Joint Services Electronics Program (Contract DAAL03-86-K-0002)Joint Services Electronics Program (Contract DAAL03-89-C-0001)U.S. Air Force - Office of Scientific Research (Grant AFOSR 86-0164)Rockwell International CorporationOKI Semiconductor, Inc.U.S. Navy - Office of Naval Research (Contract N00014-81-K-0742)Charles Stark Draper LaboratoryNational Science Foundation (Grant MIP 84-07285)National Science Foundation (Grant MIP 87-14969)Battelle LaboratoriesNational Science Foundation (Grant MIP 88-14612)DuPont CorporationDefense Advanced Research Projects Agency/U.S. Navy - Office of Naval Research (Contract N00014-87-K-0825)American Telephone and TelegraphDigital Equipment CorporationNational Science Foundation (Grant MIP-88-58764

Binary decision diagrams for fault tree analysis

This thesis develops a new approach to fault tree analysis, namely the Binary Decision Diagram (BDD) method. Conventional qualitative fault tree analysis techniques such as the "top-down" or "bottom-up" approaches are now so well developed that further refinement is unlikely to result in vast improvements in terms of their computational capability. The BDD method has exhibited potential gains to be made in terms of speed and efficiency in determining the minimal cut sets. Further, the nature of the binary decision diagram is such that it is more suited to Boolean manipulation. The BDD method has been programmed and successfully applied to a number of benchmark fault trees. The analysis capabilities of the technique have been extended such that all quantitative fault tree top event parameters, which can be determined by conventional Kinetic Tree Theory, can now be derived directly from the BDD. Parameters such as the top event probability, frequency of occurrence and expected number of occurrences can be calculated exactly using this method, removing the need for the approximations previously required. Thus the BDD method is proven to have advantages in terms of both accuracy and efficiency. Initiator/enabler event analysis and importance measures have been incorporated to extend this method into a full analysis procedure

Achieving New Upper Bounds for the Hypergraph Duality Problem through Logic

The hypergraph duality problem DUAL is defined as follows: given two simple hypergraphs $\mathcal{G}$ and $\mathcal{H}$, decide whether $\mathcal{H}$ consists precisely of all minimal transversals of $\mathcal{G}$ (in which case we say that $\mathcal{G}$ is the dual of $\mathcal{H}$). This problem is equivalent to deciding whether two given non-redundant monotone DNFs are dual. It is known that non-DUAL, the complementary problem to DUAL, is in $\mathrm{GC}(\log^2 n,\mathrm{PTIME})$, where $\mathrm{GC}(f(n),\mathcal{C})$ denotes the complexity class of all problems that after a nondeterministic guess of $O(f(n))$ bits can be decided (checked) within complexity class $\mathcal{C}$. It was conjectured that non-DUAL is in $\mathrm{GC}(\log^2 n,\mathrm{LOGSPACE})$. In this paper we prove this conjecture and actually place the non-DUAL problem into the complexity class $\mathrm{GC}(\log^2 n,\mathrm{TC}^0)$ which is a subclass of $\mathrm{GC}(\log^2 n,\mathrm{LOGSPACE})$. We here refer to the logtime-uniform version of $\mathrm{TC}^0$, which corresponds to $\mathrm{FO(COUNT)}$, i.e., first order logic augmented by counting quantifiers. We achieve the latter bound in two steps. First, based on existing problem decomposition methods, we develop a new nondeterministic algorithm for non-DUAL that requires to guess $O(\log^2 n)$ bits. We then proceed by a logical analysis of this algorithm, allowing us to formulate its deterministic part in $\mathrm{FO(COUNT)}$. From this result, by the well known inclusion $\mathrm{TC}^0\subseteq\mathrm{LOGSPACE}$, it follows that DUAL belongs also to $\mathrm{DSPACE}[\log^2 n]$. Finally, by exploiting the principles on which the proposed nondeterministic algorithm is based, we devise a deterministic algorithm that, given two hypergraphs $\mathcal{G}$ and $\mathcal{H}$, computes in quadratic logspace a transversal of $\mathcal{G}$ missing in $\mathcal{H}$.Comment: Restructured the presentation in order to be the extended version of a paper that will shortly appear in SIAM Journal on Computin