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Automated program verification often proceeds by exhibiting inductive invariants entailing the desired properties.For numerical properties, a classical class of invariants is convex polyhedra: solution sets of system of linear…
The problem of non-iterative one-shot and non-destructive correction of unavoidable mistakes arises in all Artificial Intelligence applications in the real world. Its solution requires robust separation of samples with errors from samples…
Given a sequence of $N$ positive real numbers $\{a_1,a_2,..., a_N \}$, the number partitioning problem consists of partitioning them into two sets such that the absolute value of the difference of the sums of $a_j$ over the two sets is…
We consider probabilistic automata on infinite words with acceptance defined by safety, reachability, B\"uchi, coB\"uchi, and limit-average conditions. We consider quantitative and qualitative decision problems. We present extensions and…
We realize constant-space quantum computation by measure-many two-way quantum finite automata and evaluate their language recognition power by analyzing patterns of their exotic behaviors and by exploring their structural properties. In…
In this communication, we resolve a longstanding open question in the probabilistic verification of infinite-state systems. We show that model checking {\it stateless probabilistic pushdown systems (pBPA)} against {\it probabilistic…
A data word is a sequence of pairs of a letter from a finite alphabet and an element from an infinite set, where the latter can only be compared for equality. Safety one-way alternating automata with one register on infinite data words are…
Reversible forms of computations are often interesting from an energy efficiency point of view. When the computation device in question is an automaton, it is known that the minimal reversible automaton recognizing a given language is not…
The initial-values problem of the following nonlinear autonomous recursion of order p , z (s + p) = c product of [z (s + l)]^a_l ; with p an arbitrary positive integer, z (s) the dependent variable (possibly a complex number), s the…
Random boolean cellular automata are investigated, where each gate has two randomly chosen inputs and is randomly assigned a boolean function of its inputs. The effect of non-uniform distributions on the choice of the boolean functions is…
There are many advantages to use probability method for nonlinear system identification, such as the noises and outliers in the data set do not affect the probability models significantly; the input features can be extracted in probability…
Machine learning provides algorithms that can learn from data and make inferences or predictions on data. Stochastic acceptors or probabilistic automata are stochastic automata without output that can model components in machine learning…
We present relaxed notions of simulation and bisimulation on Probabilistic Automata (PA), that allow some error epsilon. When epsilon is zero we retrieve the usual notions of bisimulation and simulation on PAs. We give logical…
We consider random boolean cellular automata on the integer lattice, i.e., the cells are identified with the integers from 1 to $N$. The behaviour of the automaton is mainly determined by the support of the random variable that selects one…
Probabilistic programs encode stochastic models as ordinary-looking programs with primitives for sampling numbers from predefined distributions and conditioning. Their applications include, among many others, machine learning and modeling…
In a probabilistic cellular automaton in which all local transitions have positive probability, the problem of keeping a bit of information indefinitely is nontrivial, even in an infinite automaton. Still, there is a solution in 2…
We are concerned with testing replicability hypotheses for many endpoints simultaneously. This constitutes a multiple test problem with composite null hypotheses. Traditional $p$-values, which are computed under least favourable parameter…
We generalize the classical probability frame by adopting a wider family of random variables that includes nondeterministic ones. The frame that emerges is known to host a ''classical'' extension of quantum mechanics. We discuss the notion…
Recursive calls over recursive data are useful for generating probability distributions, and probabilistic programming allows computations over these distributions to be expressed in a modular and intuitive way. Exact inference is also…
In this paper, a connection between bi-free probability and the theory of non-commutative stochastic processes is examined. Specifically it is demonstrated that the transition operators for non-commutative stochastic processes can be…