Complexity of Reachability for Data-Aware Dynamic Systems

It is more difficult to model a discrete system than a continuous system. Recently, a great number of applications of Petri nets to the design and the analysis of discrete systems has been reported. However, a common problem in its applications is that the required computer memories and the computation times increase explosively in accordance with the increase in the number of systems components. Some methods to divide or to reduce Petri nets have been proposed to solve this problem. Although the liveness and boundedness of Petri nets are held in the divided or reduced Petri nets, the reachability problem cannot be solved by these methods.This paper proposes another method to model discrete systems by Petri nets with place invariants. A sequential control system will be described as a typical kind of discrete system, and its structural characteristics will be used in modeling. Each component of a sequential control system will be modeled by a sub‐Petri net with place invariants. There are many components in one sequential control system, but not each one is necessarily complicated. Most sub‐Petri nets do not have so many places or transitions. It is also well known that a Petri net with place invariants is bounded and can be live by placing sufficient tokens into its initial marking. Besides, the reachability problem is not so difficult to solve in a small sub‐Petri net. Further, an activating relation to combine two or more sub‐Petri nets is defined, and some rules to reduce conflicts among enabled transitions will be described for simulations.

Immunofixation Electrophoresis (IFE) analysis is of great importance to the diagnosis of Multiple Myeloma, which is among the top-9 cancer killers in the United States, but has rarely been studied in the context of deep learning. Two possible reasons are: 1) the recognition of IFE patterns is dependent on the co-location of bands that forms a binary relation, different from the unary relation (visual features to label) that deep learning is good at modeling; 2) deep classification models may perform with high accuracy for IFE recognition but is not able to provide firm evidence (where the co-location patterns are) for its predictions, rendering difficulty for technicians to validate the results. We propose to address these issues with collocative learning, in which a collocative tensor has been constructed to transform the binary relations into unary relations that are compatible with conventional deep networks, and a location-label-free method that utilizes the Grad-CAM saliency map for evidence backtracking has been proposed for accurate localization. In addition, we have proposed Coached Attention Gates that can regulate the inference of the learning to be more consistent with human logic and thus support the evidence backtracking. The experimental results show that the proposed method has obtained a performance gain over its base model ResNet18 by 741.30% in IoU and also outperformed popular deep networks of DenseNet, CBAM, and Inception-v3.

Petri nets play a central role in the analysis of discrete, parallel and distributed systems. Reachability problem is one of the analysis of Petri nets. This paper address the analysis of reachable marking of petri nets using invariants. We translate Petri nets as transition systems. Then, through computing vanishing ideal of sample points, we present a new approach for constructing polynomial equation invariants of Petri nets. Our approach avoids first-order quantifier elimination and cylindrical algebraic decomposition. From the preliminary experiment results, we demonstrate the feasibility of our approach.

We study the complexity of the reachability problem for a new subclass of Petri nets called simple-circuit Petri nets, which properly contains several well known subclasses such as conflict-free, BPP, normal Petri nets and more. A new decomposition approach is applied to developing an integer linear programming formulation for characterizing the reachability sets of such Petri nets. Consequently, the reachability problem is shown to be NP-complete. The model checking problem for some temporal logics is also investigated for simple-circuit Petri nets.

We study the complexity of the reachability problem for a new subclass of Petri nets called simple-circuit Petri nets, which properly contains several well known subclasses such as conflict-free, BPP, normal Petri nets and more. A new decomposition approach is applied to developing an integer linear programming formulation for characterizing the reachability sets of such Petri nets. Consequently, the reachability problem is shown to be NP-complete. The model checking problem for some temporal logics is also investigated for simple-circuit Petri nets.

Working memory limits are best defined in terms of the complexity of the relations that can be processed in parallel. Complexity is defined as the number of related dimensions or sources of variation. A binary relation has one argument and one source of variation; its argument can be instantiated in only one way at a time. A binary relation has two arguments, two sources of variation, and two instantiations, and so on. Dimensionality is related to the number of chunks, because both attributes on dimensions and chunks are independent units of information of arbitrary size. Studies of working memory limits suggest that there is a soft limit corresponding to the parallel processing of one quaternary relation. More complex concepts are processed by "segmentation" or "conceptual chunking." In segmentation, tasks are broken into components that do not exceed processing capacity and can be processed serially. In conceptual chunking, representations are "collapsed" to reduce their dimensionality and hence their processing load, but at the cost of making some relational information inaccessible. Neural net models of relational representations show that relations with more arguments have a higher computational cost that coincides with experimental findings on higher processing loads in humans. Relational complexity is related to processing load in reasoning and sentence comprehension and can distinguish between the capacities of higher species. The complexity of relations processed by children increases with age. Implications for neural net models and theories of cognition and cognitive development are discussed.

Place/transition Petri nets are a standard model for a class of distributed systems whose reachability spaces might be infinite. One of well-studied topics is verification of safety and liveness properties in this model; despite an extensive research effort, some basic problems remain open, which is exemplified by the complexity status of the reachability problem that is still not fully clarified. The liveness problems are known to be closely related to the reachability problem, and various structural properties of nets that are related to liveness have been studied. Somewhat surprisingly, the decidability status of the problem of determining whether a net is structurally live, i.e. whether there is an initial marking for which it is live, remained open for some time; e.g. Best and Esparza (Inf Process Lett 116(6):423–427, 2016. https://doi.org/10.1016/j.ipl.2016.01.011 ) emphasize this open question. Here we show that the structural liveness problem for Petri nets is ExpSpace-hard and decidable. In particular, given a net N and a semilinear set S, it is decidable whether there is an initial marking of N for which the reachability set is included in S; this is based on results by Leroux (28th annual ACM/IEEE symposium on logic in computer science, LICS 2013, New Orleans, LA, USA, June 25–28, 2013, IEEE Computer Society, pp 23–32, 2013. https://doi.org/10.1109/LICS.2013.7 ).

There is no general useful method, except the reachability tree, to find legal firing sequences even for a bounded Petri net. An LP-based method with semi-polynomial-time-complexity for this problem with the m/spl times/1 known firing count vector u has been recently reported by Fujii et al (1994), but its disadvantage is that the size of constraints becomes exhaustive. For improving the above point, this paper proposes a DP-based method which can reduce about d/sup -1/ times the size of constraints for each subprocess and can also avoid the space explosion in DP by using some properties between a Petri net and its reversed net, where d is the length of firing sequence and is defined by d=/sup /spl Delta///spl Sigma//sub i=1//sup m/u/sub i/ and u=/sup /spl Delta//[u/sub i/]. Moreover, it is shown that each suboptimization can also be solved by LP with the polynomial time complexity. As a result of the above, this proposed method based on DP including d LPs is the algorithm with about d/sup -3/ times semi-polynomial time complexity compared with that given by Fujii et al. in which only one LP is applied to the given reachability problem.

When a Petri net is synthesised from a labelled transition system, it is frequently desirable that certain additional constraints are fulfilled. For example, in circuit design, one is often interested in constructing safe Petri nets. Targeting such subclasses of Petri nets is not necessarily computationally more efficient than targeting the whole class. For example, targeting safe nets is known to be NP-complete while targeting the full class of place/transition nets is polynomial, in the size of the transition system. In this paper, several classes of Petri nets are examined, and their suitability for being targeted through efficient synthesis from labelled transition systems is studied and assessed. The focus is on choice-free Petri nets and some of their subclasses. It is described how they can be synthesised efficiently from persistent transition systems, summarising and streamlining in tutorial style some of the authors’ and their groups’ work over the past few years.

Several query languages have been proposed in which users graphically manipulate Entity-Relationship (ER) diagrams to formulate queries. In this paper we present a method of implementing an ER query and update language as an interface for a relational Database Management System. The approach is based on interactive manipulation of ER database schemas and generation of SQL expressions for an underlying relational database. The graphical query and update formulation process is formally defined. We assume that the information reflecting the current state of the query and update formulation process is maintained in a formal model. The model described in other publications is significantly modified and extended. The information included in the extended model allows an ER diagram corresponding to the current state of the query to be displayed on the terminal screen. It is also used to generate an equivalent SQL expression for a relational database. The integrity constraints for the formal model are specified.

Petri nets are known to be useful for modeling concurrent systems. Once modeled by a Petri net, the behavior of a concurrent system can be characterized by the set of all executable transition sequences, which in turn can be viewed as a language over an alphabet of symbols corresponding to the transitions of the underlying Petri net. In this paper, we study the language issue of Petri nets from a computational complexity viewpoint. We analyze the complexity of theregularity problem(i.e., the problem of determining whether a given Petri net defines an irregular language or not) for a variety of classes of Petri nets, includingconflict-free,trap-circuit,normal,sinkless,extended trap-circuit,BPP, andgeneralPetri nets. (Extended trap-circuit Petri nets are trap-circuit Petri nets augmented with a specific type ofcircuits.) As it turns out, the complexities for these Petri net classes range from NL (nondeterministic logspace), PTIME (polynomial time), and NP (nondeterministic polynomial time), to EXPSPACE (exponential space). In the process of deriving the complexity results, we develop adecomposition approachwhich, we feel, is interesting in its own right, and might have other applications to the analysis of Petri nets as well. As a by-product, an NP upper bound of the reachability problem for the class of extended trap-circuit Petri nets (which properly contains that of trap-circuit (and hence, conflict-free) and BPP-nets, and is incomparable with that of normal and sinkless Petri nets) is derived.

In this paper, we develop techniques to produce interoperable queries with object and relational databases. A user poses a local query in a local query language, against a local object or relational schema. We transparently produce appropriate queries with respect to a remote target object or relational schema, corresponding to some remote database which contains data relevant to the user's query. Mapping knowledge to resolve representational heterogeneities in local and remote schemas is expressed in a canonical representation, CRmapping, and is independent of the particular data model. A canonical representation CRquery is also used to resolve heterogeneities of query languages. A set of heterogeneous transformation algorithms define the appropriate transformations from the local queries to the remote queries. The use of canonical representations (CR) allows us to represent queries independent of the particular query language, and to resolve representational conflicts in a uniform manner, independent of models and query languages.

We revisit two principal points of the book. First, objectual identity is dispensable within our conceptual scheme because Frege’s sign-based identity theory of Begriffsschrift is a viable alternative. Objections against the Begriffs-schrift conception of identity rest on misunderstandings of the ‘bifurcation in the meaning of all signs’ that comes with Frege’s view. Second, the concept of a binary identity relation between objects is incoherent, since the arity of a relation R is constrained by the Arity Principle: The arity of R is the maximal number of objects that can possibly be related by R. The maximal number of objects that can be related by objectual identity is evidently 1, since, by definition, no two objects can ever be identical. According to the Arity Principle, the only objectual identity relation is thus the unary relation (property) of self-identity.

KJ3—a tool assisting formal validation of knowledge-based systems

Exploiting partial symmetries in well-formed nets for the reachability and the linear time model checking problems