Clustering Boolean Tensors

Tensor factorizations are computationally hard problems, and in particular, are often significantly harder than their matrix counterparts. In case of Boolean tensor factorizations -- where the input tensor and all the factors are required to be binary and we use Boolean algebra -- much of that hardness comes from the possibility of overlapping components. Yet, in many applications we are perfectly happy to partition at least one of the modes. In this paper we investigate what consequences does this partitioning have on the computational complexity of the Boolean tensor factorizations and present a new algorithm for the resulting clustering problem. This algorithm can alternatively be seen as a particularly regularized clustering algorithm that can handle extremely high-dimensional observations. We analyse our algorithms with the goal of maximizing the similarity and argue that this is more meaningful than minimizing the dissimilarity. As a by-product we obtain a PTAS and an efficient 0.828-approximation algorithm for rank-1 binary factorizations. Our algorithm for Boolean tensor clustering achieves high scalability, high similarity, and good generalization to unseen data with both synthetic and real-world data sets

Quantitative Games under Failures

We study a generalisation of sabotage games, a model of dynamic network games introduced by van Benthem. The original definition of the game is inherently finite and therefore does not allow one to model infinite processes. We propose an extension of the sabotage games in which the first player (Runner) traverses an arena with dynamic weights determined by the second player (Saboteur). In our model of quantitative sabotage games, Saboteur is now given a budget that he can distribute amongst the edges of the graph, whilst Runner attempts to minimise the quantity of budget witnessed while completing his task. We show that, on the one hand, for most of the classical cost functions considered in the literature, the problem of determining if Runner has a strategy to ensure a cost below some threshold is EXPTIME-complete. On the other hand, if the budget of Saboteur is fixed a priori, then the problem is in PTIME for most cost functions. Finally, we show that restricting the dynamics of the game also leads to better complexity

An Experiment in Ping-Pong Protocol Verification by Nondeterministic Pushdown Automata

An experiment is described that confirms the security of a well-studied class of cryptographic protocols (Dolev-Yao intruder model) can be verified by two-way nondeterministic pushdown automata (2NPDA). A nondeterministic pushdown program checks whether the intersection of a regular language (the protocol to verify) and a given Dyck language containing all canceling words is empty. If it is not, an intruder can reveal secret messages sent between trusted users. The verification is guaranteed to terminate in cubic time at most on a 2NPDA-simulator. The interpretive approach used in this experiment simplifies the verification, by separating the nondeterministic pushdown logic and program control, and makes it more predictable. We describe the interpretive approach and the known transformational solutions, and show they share interesting features. Also noteworthy is how abstract results from automata theory can solve practical problems by programming language means.Comment: In Proceedings MARS/VPT 2018, arXiv:1803.0866

SystemC-based Minimum Intrusive Fault Injection Technique with Improved Fault Representation

In this paper, we propose a new SystemC-based fault injection technique that has improved fault representation in visible and on-the-fly data and signal registers. The technique is minimum intrusive since it only requires replacing the original data or signal types to fault injection enabler types. We compare the proposed simulation technique with recently reported SystemC-based techniques and show that our technique has fast simulation speed, better fault representation, while maintaining simplicity and minimum intrusion. We demonstrate fault injection capabilities in a behavioural SystemC description of MPEG-2 decoder using proposed technique and show that up to 98.9% fault representation within data and signal registers can be achieved

Contraceptive Sabotage

This Article responds to the alarm recently sounded by the American College of Obstetricians and Gynecologists over “birth control sabotage”—the “active interference [by one partner] with [the other] partner’s contraceptive methods in an attempt to promote pregnancy.” Currently, sabotage is not a crime, and existing categories of criminal offenses fail to capture the essence of the injury it does to victims. This Article argues that sabotage should be a separate crime—but only when perpetrated against those partners who can and do get pregnant as a result of having sabotaged sex. Using the principle of self-possession—understood as a person’s basic right to self-ownership—this Article argues that women have a self-possessory interest in maintaining their reproductive capacity in its non-pregnant state during and after having sex to the extent they seek to establish with the use or planned use of contraception. Sabotage by sexual partners—typically male—violates this interest and merits criminal punishment. This Article proposes statutory language to criminalize sabotage that should be added to the revision of the Model Penal Code currently underway. Not only would this addition likely survive any Equal Protection challenge, it would arguably serve to strengthen the existing constitutional right to non-procreative sex by setting meaningful limits on one partner’s ability to interfere unilaterally with the other partner’s contraceptive decisions

Clustering {Boolean} Tensors

Tensor factorizations are computationally hard problems, and in particular, are often significantly harder than their matrix counterparts. In case of Boolean tensor factorizations -- where the input tensor and all the factors are required to be binary and we use Boolean algebra -- much of that hardness comes from the possibility of overlapping components. Yet, in many applications we are perfectly happy to partition at least one of the modes. In this paper we investigate what consequences does this partitioning have on the computational complexity of the Boolean tensor factorizations and present a new algorithm for the resulting clustering problem. This algorithm can alternatively be seen as a particularly regularized clustering algorithm that can handle extremely high-dimensional observations. We analyse our algorithms with the goal of maximizing the similarity and argue that this is more meaningful than minimizing the dissimilarity. As a by-product we obtain a PTAS and an efficient 0.828-approximation algorithm for rank-1 binary factorizations. Our algorithm for Boolean tensor clustering achieves high scalability, high similarity, and good generalization to unseen data with both synthetic and real-world data sets