A New Algebraic Tool for Automatic Theorem Provers

The concepts of implicates and implicants are widely used in several fields of Automated Reasoning. Particularly, our research group has developed several techniques that allow us to reduce efficiently the size of the input, and therefore the complexity of the problem. These techniques are based on obtaining and using implicit information that is collected in terms of unitary implicates and implicants. Thus, we require efficient algorithms to calculate them. In classical propositional logic it is easy to obtain efficient algorithms to calculate the set of unitary implicants and implicates of a formula. In temporal logics, contrary to what we see in classical propositional logic, these sets may contain infinitely many members. Thus, in order to calculate them in an efficient way, we have to base the calculation on the theoretical study of how these sets behave. Such a study reveals the need to make a generalization of Lattice Theory, which is very important in Computational Algebra. In this paper we introduce the multisemilattice structure as a generalization of the semilattice structure. Such a structure is proposed as a particular type of poset. Subsequently, we offer an equivalent algebraic characterization based on non-deterministic operators and with a weakly associative property. We also show that from the structure of multisemilattice we can obtain an algebraic characterization of the multilattice structure. This paper concludes by showing the relevance of the multisemilattice structure in the design of algorithms aimed at calculating unitary implicates and implicants in temporal logics. Concretely, we show that it is possible to design efficient algorithms to calculate the unitary implicants/implicates only if the unitary formulae set has the multisemilattice structure.     

Computing prime implicants via transversal clauses

In this paper, the notion of transversal clauses is introduced and subsequently a new algorithm for computing prime implicants is developed. Opposed to the common approach of computing prime implicants of a dnf, the proposed algorithm uses a cnf representation of a propositional formula. The same algorithm applied on a dnf representation yields the set of prime implicates of a formula. Besides its suitability for implementation in a parallel environment and as an incremental algorithm, it has been found to work faster in case, the number of prime implicants is large.     

Simplification of fuzzy switching functions

This paper is concerned with the study of simplification of fuzzy switching functions. A novel algorithm for generating all fuzzy prime implicants is introduced, followed by a new method of simplification of fuzzy switching functions. This algorithm is then reduced to a simple algorithm that produces only those fuzzy prime implicants that are essential. There areonly two other valid techniques for the minimization of fuzzy switching functions in the literature,^(1,2) and those methods are not very suitable for computerized application. Thus, the principal advantages of this technique are the new concept of direct simplification via essential fuzzy prime implicants (without generation of all of the fuzzy prime implicants), and the fact that the algorithm is the first one to be suitable for efficient computer implementation.On leave from the Computer Science Department, New Mexico Institute of Mining and Technology, Socorro, New Mexico.     

Graphical scenarios for specifying temporal properties: an automated approach

Temporal logics are commonly used for reasoning about concurrent systems. Model checkers and other finite-state verification techniques allow for automated checking of system model compliance to given temporal properties. These properties are typically specified as linear-time formulae in temporal logics. Unfortunately, the level of inherent sophistication required by these formalisms too often represents an impediment to move these techniques from “research theory” to “industry practice”. The objective of this work is to facilitate the nontrivial and error prone task of specifying, correctly and without expertise in temporal logic, temporal properties. In order to understand the basis of a simple but expressive formalism for specifying temporal properties we critically analyze commonly used in practice visual notations. Then we present a scenario-based visual language called Property Sequence Chart (PSC) that, in our opinion, fixes the highlighted lacks of these notations by extending a subset of UML 2.0 Interaction Sequence Diagrams. We also provide PSC with both denotational and operational semantics. The operational semantics is obtained via translation into Büchi automata and the translation algorithm is implemented as a plugin of our Charmy tool. Expressiveness of PSC has been validated with respect to well known property specification patterns. Preliminary results appeared in (Autili et al. 2006a).     

CNF and DNF Considered Harmful for Computing Prime Implicants/Implicates

Several methods to compute the prime implicants and the prime implicates of a negation normal form (NNF) formula are developed and implemented. An algorithm PI is introduced that is an extension to negation normal form of an algorithm given by Jackson and Pais. A correctness proof of the PI algorithm is given. The PI algorithm alone is sufficient in a computational sense. However, it can be combined with path dissolution, and it is shown empirically that this is often an advantage. None of these variations rely on conjunctive normal form or on disjunctive normal form. A class of formulas is described for which reliance on CNF or on DNF results in an exponential increase in the time required to compute prime implicants/implicates. The possibility of avoiding this problem with efficient structure preserving clause form translations is examined briefly and appears unfavorable.     

Mobile broadcast services with MIMO antennae in 4G wireless networks

The deployment of wireless data broadcast to empower mobile information services as a resource-conserving means offers significant benefits due to the scalability feature offered by the technology. In this paper, we present a novel and holistic data broadcast management approach in 4 G wireless networks with multiple-input multiple-output (MIMO) antennae. The proposed scheme consists of three elements, namely: (i) broadcast ordering; (ii) Global indexing; and (iii) merging data structure. With the integration of these elements, we expect to obtain substantial efficiency for mobile computing clients when retrieving data on-air. We have experimentally evaluated the performance of the proposed model including comparison with the relevant schemes. The results from the experiments affirm the effectiveness of our proposed approach in respect to minimizing query access time and conserving energy utilization of the clients.     

A Branching Time Temporal Framework for Quantitative Reasoning

Temporal logics such as Computation Tree Logic (CTL) and Linear Temporal Logic (LTL) have become popular for specifying temporal properties over a wide variety of planning and verification problems. In this paper we work towards building a generalized framework for automated reasoning based on temporal logics. We present a powerful extension of CTL with first-order quantification over the set of reachable states for reasoning about extremal properties of weighted labeled transition systems in general. The proposed logic, which we call Weighted Quantified Computation Tree Logic (WQCTL), captures the essential elements common to the domain of planning and verification problems and can thereby be used as an effective specification language in both domains. We show that in spite of the rich, expressive power of the logic, we are able to evaluate WQCTL formulas in time polynomial in the size of the state space times the length of the formula. Wepresent experimental results on the WQCTL verifier.     

Karnaugh map analysis and synthesis of threshold functions

A unate function can easily be identified on a Karnaugh map from the well-known property that it consists only of essential prime implicants which intersect at a common implicant. The additional property that the plot of a unate function F(x₁ ?x_n ) on a Karnaugh map should possess in order that F may also be 1-realizable (n≤6) has been found. It has been shown that the 1-realizability of a unate function F corresponds to the ‘ compactness ’ of the plot of F. No resort to the inequalities is made, and no pre-processing such as positivizing and ordering of the given function is required.     

An Infinite Hierarchy of Temporal Logics over Branching Time

Many temporal logics have been suggested as branching time specification formalisms during the past 20 years. These logics were compared against each other for their expressive power, model checking complexity, and succinctness. Yet, unlike the case for linear time logics, no canonical temporal logic of branching time was agreed upon. We offer an explanation for the multiplicity of temporal logics over branching time and provide an objective quantified yardstick to measure these logics. We define an infinite hierarchy BTL_k of temporal logics and prove its strictness. We examine the expressive power of commonly used branching time temporal logics. We show that CTL* has no finite base, and that almost all of its many sublogics suggested in the literature are inside the second level of our hierarchy. We introduce new Ehrenfeucht–Fraissé games on trees and use them as our main tool to prove inexpressibility.     

A method of finding simple disjunctive decomposition with one free variable

Simple disjunctive decomposition with one free variable can be obtained by using the prime implicants of the Boolean function. A function is decomposable with its redundant variable as a free variable. A necessary condition for decomposition with a non-redundant variable as free variable is that the number of minterms in an n variable function be 2^(n?1). A sufficient condition is that the variable remain present, in either true or complemented form, in all the prime implicants of the function.     

A Polynomial Model for Logics with a Prime Power Number of Truth Values

This paper is concerned with a polynomial model (residue class ring) for a given q-valued propositional logic (where q is a power of a prime integer). This model allows to transfer logic problems into algebraic terms, resulting in an immediate computational approach to Knowledge Based Systems based on multi-valued logics. By means of this new approach, we have extended an already existent algebraic model to logics with a prime power number of truth values, while also getting more straightforward proofs and a more direct enunciation of the central theorem of this model.     

A multiagent framework for coordinated parallel problem solving

Today’s organizations, under increasing pressure on the effectiveness and the increasing need for dealing with complex tasks beyond a single individual’s capabilities, need technological support in managing complex tasks that involve highly distributed and heterogeneous information sources and several actors. This paper describes CoPSF, a multiagent system middle-ware that simplifies the development of coordinated problem solving applications while ensuring standard compliance through a set of system services and agents. CoPSF hosts and serves multiple concurrent teams of problem solving contributing both to the limitation of communication overheads and to the reduction of redundant work across teams and organizations. The framework employs (i) an interleaved task decomposition and allocation approach, (ii) a mechanism for coordination of agents’ work, and (iii) a mechanism that enables synergy between parallel teams.     

Decomposition of graphs and monotone formula size of homogeneous functions

Summary We show that every graph on n nodes can be partitioned by a number of complete bipartite graphs with O(n ²/log n) nodes with no edge belonging to two of them. Since each partition corresponds directly to a monotone formula for the associated quadratic function we obtain an upper bound for the monotone formula size of quadratic functions. Our method extends to uniform hypergraphs with fixed range and thus to homogeneous functions with fixed length of prime implicants. Finally we give an example of a quadratic function where each monotone formula built from arbitrary partitions of the graph (double edges allowed) is not optimal. That means we disprove the single-level-conjecture for formulae.     

Useless prime implicants of incompletely specified multiple-output switching functions

In the process of finding a minimal sum representation for an incompletely specified multiple-output switching function, there often occur certain types of prime implicants, referred to as useless, which can be discarded because of the presence of the don't-cares. This paper presents a correction to the definition of useless given by Tison and extends the definition to other notations. A procedure for removing useless prime implicants quickly is presented for the case when multiple-output prime implicants are derived from minterms. The deletion of useless prime implicants can, in many cases, speed up any procedure for finding a minimal sum that begins with the multiple-output prime implicants in both hand calculation and in computer implementation.This work was supported in part by the National Science Foundation under Grant No. MCS-77-09744.     

Spherical image QoE approximations for vision augmentation scenarios

Augmented Reality (AR) devices are commonly head-worn to overlay context-dependent information into the field of view of the device operators. One particular scenario is the overlay of still images, for which we evaluate the interplay of user ratings as Quality of Experience (QoE) with (i) the non-referential BRISQUE objective image quality metric as Quality of Service (QoS) and (ii) human subject dry electrode EEG signals gathered with a commercial off-the-shelf device. We employ basic machine learning approaches to perform QoE and QoS predictions based on this data. We find strong correlations for QoS inputs with aggregated user ratings as Mean Opinion Scores with spherical images. For subject-specific EEG portfolios, overall predictability of the QoE for both media types can be attained. Our overall results can be employed in practical scenarios by content and network service providers to optimize the user experience in augmented reality scenarios with a passive human in-the-loop in the future.

     

Interpretability of first-order linear temporal logics in fork algebras

In this paper we prove theorems on the interpretability of the first-order temporal logics LTL and TL into Fork Algebras. This result is part of a research project on the interpretability of logics in Fork Algebras, and has important applications towards the relational specification of properties of systems within the Ar_gentum tool.     

Defeating Colluding Nodes in Desktop Grid Computing Platforms

Desktop Grid systems reached a preeminent place among the most powerful computing platforms in the planet. Unfortunately, they are extremely vulnerable to mischief, because computing projects exert no administrative or technical control on volunteers. These can very easily output bad results, due to software or hardware glitches (resulting from over-clocking for instance), to get unfair computational credit, or simply to ruin the project. To mitigate this problem, Desktop Grid servers replicate work units and apply majority voting, typically on 2 or 3 results. In this paper, we observe that simple majority voting is powerless against malicious volunteers that collude to attack the project. We argue that to identify this type of attack and to spot colluding nodes, each work unit needs at least 3 voters. In addition, we propose to post-process the voting pools in two steps. i) In the first step, we use a statistical approach to identify nodes that were not colluding, but submitted bad results; ii) then, we use a rather simple principle to go after malicious nodes which acted together: they might have won conflicting voting pools against nodes that were not identified in step i. We use simulation to show that our heuristic can be quite effective against colluding nodes, in scenarios where honest nodes form a majority.     

On reducing the number of stack symbols in a PDA

Two transformations are presented which, for any pushdown automaton (PDA)M withn states andp stack symbols, reduce the number of stack symbols to any desired numberp greater than one. The first transformation preserves deterministic behavior and produces an equivalent PDA witho(np/p) states. The second construction, using a technique which introduces nondeterminism, produces an equivalent PDA withO(np/p) states. Both transformations are essentially optimal, the former among determinism-preserving transformations, the latter among all transformations.This research was supported in part by the National Science Foundation under Grants MCS 76-10076 and MCS 76-10076A01 and by the Stiftung Volkswagenwerk under Grant No. II/62 325.     

Minimum Initial Marking Estimation of Labeled Petri Nets Based on GRASP Inspired Method (GMIM)

Abstract

This paper deals with the problem of estimating the Minimum Initial Marking (MIM) of Labeled Petri Nets (L-PN). By the observation of a sequence of labels, we determine the set of possible MIMs related to a given L-PN through an approach based on GRASP (Greedy Randomized Adaptive Search Procedure) inspired method – GMIM. The objective is to get the maximum of feasible MIMs by exploring the search space and giving best solutions for real time cyber systems in short time. We consider four basic assumptions during the reasoning: (i) the L-PN structure is known; (ii) for each transition of L-PN, a label is associated, (iii) the label sequence is known, and (iv) all transitions of L-PN are observable. We show the validity and efficiency of our approach by applying the proposed GMIM metaheuristic to two validation examples: Initialization of two parallel machines (example widely cited in literature) and resources allocation in a monitoring problem via mobile robot network.