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Knowledge compilation is an approach to tackle the computational intractability of general reasoning problems. According to this approach, knowledge bases are converted off-line into a target compilation language which is tractable for…
Combining ideas from distributed algorithms and alternating automata, we introduce a new class of finite graph automata that recognize precisely the languages of finite graphs definable in monadic second-order logic. By restricting…
This note is an attempt to unconditionally prove the existence of weak one way functions (OWF). Starting from a provably intractable decision problem $L_D$ (whose existence is nonconstructively assured from the well-known discrete…
A recently proposed canonical form of Boolean functions, namely tagged sentential decision diagrams (TSDDs), exploits both the standard and zero-suppressed trimming rules. The standard ones minimize the size of sentential decision diagrams…
The advanced data structure of the zero-suppressed binary decision diagram (ZDD) enables us to efficiently enumerate nonequivalent substitutional structures. Not only can the ZDD store a vast number of structures in a compressed manner, but…
A derivative structure is a nonequivalent substitutional atomic configuration derived from a given primitive cell. The enumeration of derivative structures plays an essential role in searching for the ground states in multicomponent…
We introduce the affine OBDD model and show that zero-error affine OBDDs can be exponentially narrower than bounded-error unitary and probabilistic OBDDs on certain problems. Moreover, we show that Las Vegas unitary and probabilistic OBDDs…
A conjunctive Boolean network (CBN) is a finite state dynamical system, whose variables take values from a binary set, and the value update rule for each variable is a Boolean function consisting only of logic AND operations. We investigate…
We propose an approach for explaining Bayesian network classifiers, which is based on compiling such classifiers into decision functions that have a tractable and symbolic form. We introduce two types of explanations for why a classifier…
Boolean networks can be viewed as functions on the set of binary strings of a given length, described via logical rules. They were introduced as dynamic models into biology, in particular as logical models of intracellular regulatory…
The lower and upper bound of any given algorithm is one of the most crucial pieces of information needed when evaluating the computational effectiveness for said algorithm. Here a novel method of Boolean Algebraic Programming for symbolic…
Data-driven modelling and scientific machine learning have been responsible for significant advances in determining suitable models to describe data. Within dynamical systems, neural ordinary differential equations (ODEs), where the system…
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…
In this paper, we study quantum Ordered Binary Decision Diagrams($OBDD$) model; it is a restricted version of read-once quantum branching programs, with respect to "width" complexity. It is known that the maximal gap between deterministic…
Anomaly detection (AD) plays a pivotal role in numerous web-based applications, including malware detection, anti-money laundering, device failure detection, and network fault analysis. Most methods, which rely on unsupervised learning, are…
Decision Diagrams(DDs) are one of the most popular representations for boolean functions. They are widely used in the design and verification of circuits. Different types of DDs have been proven to represent important functions in…
BDDs are representations of a Boolean expression in the form of a directed acyclic graph. BDDs are widely used in several fields, particularly in model checking and hardware verification. There are several implementations for BDD…
Time-delay systems are an important class of dynamical systems which provide a solid mathematical framework to deal with many application domains of interest ranging from biology, chemical, electrical, and mechanical engineering, to…
Symbolic models are abstract descriptions of continuous systems in which symbols represent aggregates of continuous states. In the last few years there has been a growing interest in the use of symbolic models as a tool for mitigating…
We define an odometer in the Baire space. That is the non-compact space of one sided sequences of natural numbers. We go on to prove that it is topologically conjugated to the dyadic odometer restricted to an appropriate non-compact subset…