Related papers: Parikh's Theorem Made Symbolic
This paper presents two concrete applications of Artificial Intelligence to algorithmic and analytic number theory. Recent benchmarks of large language models have mainly focused on general mathematics problems and the currently infeasible…
Tabling in logic programming has been used to eliminate redundant computation and also to stop infinite loop. In this paper we investigate another possibility of tabling, i.e. to compute an infinite sum of probabilities for probabilistic…
For logic programs with arithmetic predicates, showing termination is not easy, since the usual order for the integers is not well-founded. A new method, easily incorporated in the TermiLog system for automatic termination analysis, is…
An important open question in AI is what simple and natural principle enables a machine to reason logically for meaningful abstraction with grounded symbols. This paper explores a conceptually new approach to combining probabilistic…
This paper analyzes the correctness of the subsumption algorithm used in CLASSIC, a description logic-based knowledge representation system that is being used in practical applications. In order to deal efficiently with individuals in…
We investigate the computational power of particle methods, a well-established class of algorit hms with applications in scientific computing and computer simulation. The computational power of a compute model determines the class of…
Probabilistic programming combines general computer programming, statistical inference, and formal semantics to help systems make decisions when facing uncertainty. Probabilistic programs are ubiquitous, including having a significant…
Engelfriet and Vereijken have shown that linear graph grammars based on hyperedge replacement generate graph languages that can be considered as interpretations of regular string languages over typed symbols. In this paper we show that…
We give a quantifier elimination procedure for one-parametric Presburger arithmetic, the extension of Presburger arithmetic with the function $x \mapsto t \cdot x$, where $t$ is a fixed free variable ranging over the integers. This resolves…
{log} ('setlog') is a satisfiability solver for formulas of the theory of finite sets and finite set relation algebra (FSTRA). As such, it can be used as an automated theorem prover (ATP) for this theory. {log} is able to automatically…
Given a formula in quantifier-free Presburger arithmetic, if it has a satisfying solution, there is one whose size, measured in bits, is polynomially bounded in the size of the formula. In this paper, we consider a special class of…
We present counting reward automata-a finite state machine variant capable of modelling any reward function expressible as a formal language. Unlike previous approaches, which are limited to the expression of tasks as regular languages, our…
The downward closure of a language $L$ of words is the set of all (not necessarily contiguous) subwords of members of $L$. It is well known that the downward closure of any language is regular. Although the downward closure seems to be a…
Parameter learning is a crucial task in the field of Statistical Relational Artificial Intelligence: given a probabilistic logic program and a set of observations in the form of interpretations, the goal is to learn the probabilities of the…
The combination of uninterpreted function symbols and universal quantification occurs in many applications of automated reasoning, for example, due to their ability to reason about arrays. Yet the satisfiability of such formulas is, in…
Logic languages based on the theory of rational, possibly infinite, trees have much appeal in that rational trees allow for faster unification (due to the safe omission of the occurs-check) and increased expressivity (cyclic terms can…
A cost Markov chain is a Markov chain whose transitions are labelled with non-negative integer costs. A fundamental problem on this model, with applications in the verification of stochastic systems, is to compute information about the…
A summation framework is developed that enhances Karr's difference field approach. It covers not only indefinite nested sums and products in terms of transcendental extensions, but it can treat, e.g., nested products defined over roots of…
Let D denote an infinite alphabet -- a set that consists of infinitely many symbols. A word w = a_0 b_0 a_1 b_1 ... a_n b_n of even length over D can be viewed as a directed graph G_w whose vertices are the symbols that appear in w, and the…
In a previous paper, we have shown that any Boolean formula can be encoded as a linear programming problem in the framework of Bayesian probability theory. When applied to NP-complete algorithms, this leads to the fundamental conclusion…