Related papers: Uncountable realtime probabilistic classes
We consider a general class of decision problems concerning formal languages, called ``(one-dimensional) unboundedness predicates'', for automata that feature reversal-bounded counters (RBCA). We show that each problem in this class reduces…
We present new results on the landscape of problems that can be solved by quantum Turing machines (QTM's) employing severely limited amounts of memory. In this context, we demonstrate two infinite time hierarchies of complexity classes…
This work addresses the problem of computing measures of recognisable sets of infinite trees. An algorithm is provided to compute the probability measure of a tree language recognisable by a weak alternating automaton, or equivalently…
Many probabilistic programming languages allow programs to be run under constraints in order to carry out Bayesian inference. Running programs under constraints could enable other uses such as rare event simulation and probabilistic…
We create a new online reduction of multiclass classification to binary classification for which training and prediction time scale logarithmically with the number of classes. Compared to previous approaches, we obtain substantially better…
Linear temporal logic (LTL) is a specification language for finite sequences (called traces) widely used in program verification, motion planning in robotics, process mining, and many other areas. We consider the problem of learning LTL…
We study the capabilities of probabilistic finite-state machines that act as verifiers for certificates of language membership for input strings, in the regime where the verifiers are restricted to toss some fixed nonzero number of coins…
Constrained counting is important in domains ranging from artificial intelligence to software analysis. There are already a few approaches for counting models over various types of constraints. Recently, hashing-based approaches achieve…
We show that one can approximate the least fixed point solution for a multivariate system of monotone probabilistic polynomial equations in time polynomial in both the encoding size of the system of equations and in log(1/\epsilon), where…
Suppose a language $L$ can be decided by a bounded-error randomized algorithm that runs in space $S$ and time $n \cdot \text{poly}(S)$. We give a randomized algorithm for $L$ that still runs in space $O(S)$ and time $n \cdot \text{poly}(S)$…
We introduce a novel quantum programming language featuring higher-order programs and quantum controlflow which ensures that all qubit transformations are unitary. Our language boasts a type system guaranteeingboth unitarity and…
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…
Designing models that are both expressive and preserve known invariances of tasks is an increasingly hard problem. Existing solutions tradeoff invariance for computational or memory resources. In this work, we show how to leverage…
Condon and Lipton (FOCS 1989) showed that the class of languages having a space-bounded interactive proof system (IPS) is a proper subset of decidable languages, where the verifier is a probabilistic Turing machine. In this paper, we show…
This paper explores the space of (propositional) probabilistic logical languages, ranging from a purely `qualitative' comparative language to a highly `quantitative' language involving arbitrary polynomials over probability terms. While…
For any particularly interesting theorem one proof is never enough. Instead, the first proof sets the challenge to find a more elegant method that illuminates subtle features of the math, is simpler to understand, or even avoids using…
We present two new results on the computational limitations of affine automata. First, we show that the computation of bounded-error rational-values affine automata is simulated in logarithmic space. Second, we give an impossibility result…
Modern language models predict the next token in the sequence by considering the past text through a powerful function such as attention. However, language models have no explicit mechanism that allows them to spend computation time for…
In this thesis, we introduce a new quantum Turing machine (QTM) model that supports general quantum operators, together with its pushdown, counter, and finite automaton variants, and examine the computational power of classical and quantum…
In [1], we introduced the weakly synchronizing languages for probabilistic automata. In this report, we show that the emptiness problem of weakly synchronizing languages for probabilistic automata is undecidable. This implies that the…