Related papers: Parikh's Theorem Made Symbolic
This paper gives a decision procedure for the validity of en- tailment of symbolic heaps in separation logic with Presburger arithmetic and arrays. The correctness of the decision procedure is proved under the condition that sizes of arrays…
Quantitative automata model beyond-boolean aspects of systems: every execution is mapped to a real number by incorporating weighted transitions and value functions that generalize acceptance conditions of boolean $\omega$-automata. Despite…
We characterize the meaning of words with language-independent numerical fingerprints, through a mathematical analysis of recurring patterns in texts. Approximating texts by Markov processes on a long-range time scale, we are able to…
Many representation schemes combining first-order logic and probability have been proposed in recent years. Progress in unifying logical and probabilistic inference has been slower. Existing methods are mainly variants of lifted variable…
The PCP Theorem is one of the most stunning results in computational complexity theory, a culmination of a series of results regarding proof checking it exposes some deep structure of computational problems. As a surprising side-effect, it…
This paper provides a definitive, unifying framework for the Symbol Grounding Problem (SGP) by reformulating it within Algorithmic Information Theory (AIT). We demonstrate that the grounding of meaning is a process fundamentally constrained…
Programming languages tend to evolve over time to use more and more concepts from theoretical computer science. Still, there is a gap between programming and pure mathematics. Not all theoretical results have realized their promising…
The unification algorithm has long been a target for program synthesis research, but a fully automatic derivation remains a research goal. In deductive program synthesis, computer programming is phrased as a task in theorem proving; a…
Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…
In the last ten years, the employment of symbolic methods has substantially extended both the theory and the applications of statistics and probability. This survey reviews the development of a symbolic technique arising from classical…
We present a new approach to automated reasoning about higher-order programs by extending symbolic execution to use behavioral contracts as symbolic values, enabling symbolic approximation of higher-order behavior. Our approach is based on…
We propose a new symbolic trace semantics for register automata (extended finite state machines) which records both the sequence of input symbols that occur during a run as well as the constraints on input parameters that are imposed by…
In this paper, we consider the satisfiability problem for string logic with equations, regular membership and Presburger constraints over length functions. The difficulty comes from multiple occurrences of string variables making…
Alternating automata have been widely used to model and verify systems that handle data from finite domains, such as communication protocols or hardware. The main advantage of the alternating model of computation is that complementation is…
We study the computational and descriptional complexity of the following transformation: Given a one-counter automaton (OCA) A, construct a nondeterministic finite automaton (NFA) B that recognizes an abstraction of the language L(A): its…
Large language models (LLMs) have recently demonstrated an impressive ability to perform arithmetic and symbolic reasoning tasks, when provided with a few examples at test time ("few-shot prompting"). Much of this success can be attributed…
Usually, probabilistic automata and probabilistic grammars have crisp symbols as inputs, which can be viewed as the formal models of computing with values. In this paper, we first introduce probabilistic automata and probabilistic grammars…
Parikh's game logic is a PDL-like fixpoint logic interpreted on monotone neighbourhood frames that represent the strategic power of players in determined two-player games. Game logic translates into a fragment of the monotone…
We introduce an automata-theoretic method for the verification of distributed algorithms running on ring networks. In a distributed algorithm, an arbitrary number of processes cooperate to achieve a common goal (e.g., elect a leader).…
This paper studies the complexity of languages of finite words using automata theory. To go beyond the class of regular languages, we consider infinite automata and the notion of state complexity defined by Karp. Motivated by the seminal…