Related papers: Regular realizability problems and regular languag…
In this paper we treat the specification problem in classical realizability (as defined in [20]) in the case of arithmetical formul{\ae}. In the continuity of [10] and [11], we characterize the universal realizers of a formula as being the…
In this article, we prove the following interpolation problem: if the composition of a function and a regular map between affine varieties is a regular function, then there exists a global regular function of the target variety that…
We consider algorithms and lower bounds for various problems over forest languages; as input models we allow forest algebras, deterministic forest automata and nondeterministic forest automata. For the equivalence problem, we give an…
We investigate the complexity of the reachability problem for (deep) neural networks: does it compute valid output given some valid input? It was recently claimed that the problem is NP-complete for general neural networks and conjunctive…
Regular resolution is a refinement of the resolution proof system requiring that no variable be resolved on more than once along any path in the proof. It is known that there exist sequences of formulas that require exponential-size proofs…
The ambiguity of a nondeterministic finite automaton (NFA) N for input size n is the maximal number of accepting computations of N for an input of size n. For all k, r 2 N we construct languages Lr,k which can be recognized by NFA's with…
The theory of classical realizability is a framework in which we can develop the proof-program correspondence. Using this framework, we show how to transform into programs the proofs in classical analysis with dependent choice and the…
With the proliferation of Deep Machine Learning into real-life applications, a particular property of this technology has been brought to attention: robustness Neural Networks notoriously present low robustness and can be highly sensitive…
One of my recent papers transforms an NP-Complete problem into the question of whether or not a feasible real solution exists to some Linear Program. The unique feature of this Linear Program is that though there is no explicit bound on the…
In a typical regular expression (regex) crossword puzzle, you are given two nonempty lists $R_1,\ldots,R_m$ and $C_1,\ldots,C_n$ of regular expressions over some alphabet, and your goal is to fill in an $m\times n$ grid with letters from…
We study the problem of regular separability of languages of vector addition systems with states (VASS). It asks whether for two given VASS languages K and L, there exists a regular language R that includes K and is disjoint from L. While…
In a recent thread of papers, we have introduced FQL, a precise specification language for test coverage, and developed the test case generation engine FShell for ANSI C. In essence, an FQL test specification amounts to a set of regular…
For typical first-order logical theories, satisfying assignments have a straightforward finite representation that can directly serve as a certificate that a given assignment satisfies the given formula. For non-linear real arithmetic…
We investigate the internal representations that a recurrent neural network (RNN) uses while learning to recognize a regular formal language. Specifically, we train a RNN on positive and negative examples from a regular language, and ask if…
We analyse the complexity of the satisfiability problem, or similarly feasibility problem, (trSAT) for transformer encoders (TE), which naturally occurs in formal verification or interpretation, collectively referred to as formal reasoning.…
It is common practice in reinforcement learning (RL) research to train and deploy agents in bespoke simulators, typically implemented by engineers directly in general-purpose programming languages or hardware acceleration frameworks such as…
A common standpoint when designing the syntax of programming languages is that the grammar definition has to be unambiguous. However, requiring up front unambiguous grammars can force language designers to make more or less arbitrary…
A class of languages C is perfect if it is closed under Boolean operations and the emptiness problem is decidable. Perfect language classes are the basis for the automata-theoretic approach to model checking: a system is correct if the…
In recent years some researchers have explored the use of reinforcement learning (RL) algorithms as key components in the solution of various natural language processing tasks. For instance, some of these algorithms leveraging deep neural…
The success of many natural language processing (NLP) tasks is bound by the number and quality of annotated data, but there is often a shortage of such training data. In this paper, we ask the question: "Can we combine a neural network (NN)…