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The size and complexity of software and hardware systems have significantly increased in the past years. As a result, it is harder to guarantee their correct behavior. One of the most successful methods for automated verification of…
Temporal Logic Model Checking is a verification method in which we describe a system, the model, and then we verify whether some properties, expressed in a temporal logic formula, hold in the system. It has many industrial applications. In…
Markov decisions processes (MDPs) are becoming increasing popular as models of decision theoretic planning. While traditional dynamic programming methods perform well for problems with small state spaces, structured methods are needed for…
We propose a method for testing whether hierarchically ordered groups of potentially correlated variables are significant for explaining a response in a high-dimensional linear model. In presence of highly correlated variables, as is very…
Symbolic model checking by using BDDs has greatly improved the applicability of model checking. Nevertheless, BDD based symbolic model checking can still be very memory and time consuming. One main reason is the complex transition relation…
Model checking has been proposed as a formal verification approach for analyzing computer-based and cyber-physical systems. The state space explosion problem is the main obstacle for applying this approach for sophisticated systems.…
Ordered binary decision diagrams (OBDDs) are a fundamental data structure for the manipulation of Boolean functions, with strong applications to finite-state symbolic model checking. OBDDs allow for efficient algorithms using top-down…
Decision diagrams (DDs) are a powerful data structure that is used to tackle the state-space explosion problem, not only for discrete systems, but for probabilistic and quantum systems as well. While many of the DDs used in the…
Decision diagram (DD)-based quantum circuit simulators represent quantum states and gates using DDs, enabling memory-efficient and fast simulations for some quantum circuits like Shor. Although it is known that DD size and processing time…
Binary decision diagrams can compactly represent vast sets of states, mitigating the state space explosion problem in model checking. Probabilistic systems, however, require multi-terminal diagrams storing rational numbers. They are…
One technique to reduce the state-space explosion problem in temporal logic model checking is symmetry reduction. The combination of symmetry reduction and symbolic model checking by using BDDs suffered a long time from the prohibitively…
We use dense variable-ordering to define HRD (Hybrid-Restriction Diagram), a new BDD-like data-structure for the representation and manipulation of state-spaces of linear hybrid automata. We present and discuss various manipulation…
Symbolic execution is a powerful technique for analyzing the behavior of software yet scalability remains a challenge due to state explosion in control and data flow. Existing tools typically aim at managing control flow internally, often…
Symbolic computation, powered by modern computer algebra systems, has important applications in mathematical reasoning through exact deep computations. The efficiency of symbolic computation is largely constrained by such deep computations…
The control design tools for linear systems typically involves pole placement and computing Lyapunov functions which are useful for ensuring stability. But given higher requirements on control design, a designer is expected to satisfy other…
Dynamic programming algorithms have been successfully applied to propositional stochastic planning problems by using compact representations, in particular algebraic decision diagrams, to capture domain dynamics and value functions. Work on…
Large scale dynamical systems (e.g. many nonlinear coupled differential equations) can often be summarized in terms of only a few state variables (a few equations), a trait that reduces complexity and facilitates exploration of behavioral…
In big data analysis, a simple task such as linear regression can become very challenging as the variable dimension $p$ grows. As a result, variable screening is inevitable in many scientific studies. In recent years, randomized algorithms…
The utilization of model checking has been suggested as a formal verification technique for analyzing critical systems. However, the primary challenge in applying to complex systems is state space explosion problem. To address this issue,…
Finding statistically significant interactions between binary variables is computationally and statistically challenging in high-dimensional settings, due to the combinatorial explosion in the number of hypotheses. Terada et al. recently…