Related papers: The existence of a near-unanimity function is deci…
"Unidirectional channel systems" (Chambart & Schnoebelen, CONCUR 2008) are finite-state systems where one-way communication from a Sender to a Receiver goes via one reliable and one unreliable unbounded fifo channel. While reachability is…
This paper deals with formulas of set theory which force the infinity. For such formulas, we provide a technique to infer satisfiability from a finite assignment.
This unpublished note is an alternate, shorter (and hopefully more readable) proof of the decidability of all minimal models. The decidability follows from a proof of the existence of a cellular term in each observational equivalence class…
Existence of an increasing quasi-concave value function consistent with given preference information is an important issue in various fields including Economics, Multiple Criteria Decision Making, and Applied Mathematics. In this paper, we…
We consider the decidability of state-to-state reachability in linear time-invariant control systems over discrete time. We analyse this problem with respect to the allowable control sets, which in general are assumed to be defined by…
In this paper we solve the satisfiability problem of an extended fragment of set computable theory which "forces the infinity" by a fruitful use of the witness small model property and the theory of formative processes.
For a poset $(P,\leqslant)$ we consider the first-order theory, that is defined by set $P$ and relation $\leqslant$. The problem of undecidability of combinatorial theories attracts significant attention. Recently A. Wires proved the…
Functions that are piecewise defined are a common sight in mathematics while convexity is a property especially desired in optimization. Suppose now a piecewise-defined function is convex on each of its defining components - when can we…
Mateescu, Salomaa, and Yu asked: is it decidable whether a given subword history assumes only non-negative values for all words over a given alphabet. In this paper, we solve this open problem by proving that this problem is undecidable…
A family of asymptotic solutions at infinity for the system of ordinary differential equations is considered. Existence of exact solutions which have these asymptotics is proved.
The uncertainty relation, as one of the fundamental principles of quantum physics, captures the incompatibility of noncommuting observables in the preparation of quantum states. In this work, we derive two strong and universal uncertainty…
Representable implication algebras are known to be axiomatised by a finite number of equations (making the representation and finite representation problems decidable here). We show that this also holds in the context of unary (and binary)…
We give a simple proof that the first-order theory of well orders is axiomatized by transfinite induction, and that it is decidable.
The essential variables in a finite function $f$ are defined as variables which occur in $f$ and weigh with the values of that function. The number of essential variables is an important measure of complexity for discrete functions. When…
In this paper we prove undecidability of finite systems of equations in free Lie algebras of rank at least three over an arbitrary field. We show that the ring of integers $\mathbb{Z}$ is interpretable by positive existential formulas in…
Given a set B of finite rooted graphs and a radius r as an input, we prove that it is undecidable to determine whether there exists a sequence (G_i) of finite bounded degree graphs such that the rooted r-radius neighbourhood of a random…
We introduce the notion of uniform exactness, or uniform amenability at infinity, for discrete groups and prove it for a wide class of groups containing free groups and their limit groups. This shows a novel strong convergence phenomenon…
In this paper, we show that a partitioned formula \phi is dependent if and only if \phi has uniform definability of types over finite partial order indiscernibles. This generalizes our result from a previous paper [1]. We show this by…
This paper deals with the problem of point-to-point reachability in multi-linear systems. These systems consist of a partition of the Euclidean space into a finite number of regions and a constant derivative assigned to each region in the…
The "finite intersection property" for bifunctions is introduced and its relationship with generalized monotonicity properties is studied. Some results concerning existence of solution for (quasi-)equilibrium problems are established and…