Related papers: Ultimate periodicity problem for linear numeration…
We study the following natural variation on the classical universality problem: given a language $L(M)$ represented by $M$ (e.g., a DFA/RE/NFA/PDA), does there exist an integer $\ell \geq 0$ such that $\Sigma^\ell \subseteq L(M)$? In the…
We consider probabilistic automata on infinite words with acceptance defined by parity conditions. We consider three qualitative decision problems: (i) the positive decision problem asks whether there is a word that is accepted with…
The value 1 problem is a decision problem for probabilistic automata over finite words: given a probabilistic automaton A, are there words accepted by A with probability arbitrarily close to 1? This problem was proved undecidable recently.…
For a given intuitionistic propositional formula A and a propositional variable x occurring in it, define the infinite sequence of formulae { A \_i | i$\ge$1} by letting A\_1 be A and A\_{i+1} be A(A\_i/x). Ruitenburg's Theorem [8] says…
Due to the undecidability of most type-related properties of System F like type inhabitation or type checking, restricted polymorphic systems have been widely investigated (the most well-known being ML-polymorphism). In this paper we…
We consider linear systems of recurrence equations whose coefficients are given in terms of indefinite nested sums and products covering, e.g., the harmonic numbers, hypergeometric products, $q$-hypergeometric products or their mixed…
It is well known that the emptiness problem for binary probabilistic automata and so for quantum automata is undecidable. We present the current status of the emptiness problems for unary probabilistic and quantum automata with connections…
This paper is proposing a general periodicity result concerning any deterministic and memoryless scheduling algorithm (including non-work-conserving algorithms), for any context, on identical multiprocessor platforms. By context we mean the…
In this paper we consider a number of natural decision problems involving k-regular sequences. Specifically, they arise from - lower and upper bounds on growth rate; in particular boundedness, - images, - regularity (recognizability by a…
We consider an exhaustive polling system with three nodes in its transient regime under a switching rule of generalized greedy type. We show that, for the system with Poisson arrivals and service times with finite second moment, the…
In this paper, we study the periodicity structure of finite field linear recurring sequences whose period is not necessarily maximal and determine necessary and sufficient conditions for the characteristic polynomial~\(f\) to have exactly…
We develop an experimental algorithm for the exact solving of the maximum independent set problem. The algorithm consecutively finds the maximal independent sets of vertices in an arbitrary undirected graph such that the next such set…
The show that the upper-left-corner problem and upper-right-corner problem for matrix groups with rational entries are undecidable. To reach this aim, we answer a question of Dixon from 1985 by proving the undecidability of the stabilizer…
We study the problem of completely automatically verifying uninterpreted programs---programs that work over arbitrary data models that provide an interpretation for the constants, functions and relations the program uses. The verification…
Ruitenburg's Theorem says that every endomorphism f of a finitely generated free Heyting algebra is ultimately periodic if f fixes all the generators but one. More precisely, there is N $\ge$ 0 such that f N +2 = f N , thus the period…
In this paper, we present a proof of the NP-completeness of computing the smallest Deterministic Finite Automaton (DFA) that distinguishes two given regular languages as DFAs. A distinguishing DFA is an automaton that recognizes a language…
This work is concerned with the identification problem for what we call the perturbation term or error term in a parabolic partial differential equation, through its approximate periodic solutions. The observation is made over a subregion…
Classes of polynomial differential equations of degree n are considered. An explicit upper bound on the size of the coefficients are given which implies that each equation in the class has exactly n complex periodic solutions. In most of…
We show that the problem `whether a finite set of regular-linear axioms defines a rigid theory' is undecidable.
In this paper we propose some continuation theorems for the periodic problem \begin{equation*} \begin{cases} \, x_{i}' = g_{i}(t,x_{i+1}), &i=1,\ldots,n-1, \\ \, x_{n}' = h(t,x_{1},\ldots,x_{n}), \\ \, x_{i}(0)=x_{i}(T), &i=1,\ldots,n,…