Related papers: SLD-resolution without occur-check, an example
A cyclic proof system is a proof system whose proof figure is a tree with cycles. The cut-elimination in a proof system is fundamental. It is conjectured that the cut-elimination in the cyclic proof system for first-order logic with…
We consider in this paper a class of composite optimization problems whose objective function is given by the summation of a general smooth and nonsmooth component, together with a relatively simple nonsmooth term. We present a new class of…
The current scenario in the field of computing is largely affected by the speed at which data can be accessed and recalled. In this paper, we present the word existence algorithm which is used to check if the word given as an input is part…
Sequential testing problems involve a complex system with several components, each of which is "working" with some independent probability. The outcome of each component can be determined by performing a test, which incurs some cost. The…
Recent LLMs have significantly improved reasoning capabilities, primarily by including an explicit, lengthy Thinking process as part of generation. In this paper, we question whether this explicit thinking is necessary. Using the…
For a class L of languages let PDL[L] be an extension of Propositional Dynamic Logic which allows programs to be in a language of L rather than just to be regular. If L contains a non-regular language, PDL[L] can express non-regular…
When optimizing a thread in a concurrent program (either done manually or by the compiler), it must be guaranteed that the resulting thread is a refinement of the original thread. Most theories of valid optimizations are formulated in terms…
We develop an algorithm for parameter-free stochastic convex optimization (SCO) whose rate of convergence is only a double-logarithmic factor larger than the optimal rate for the corresponding known-parameter setting. In contrast, the best…
Side-channel attacks are a major threat to the security of cryptosystems. Masking is a widely used countermeasure against such attacks, but proving the security of masked algorithms is error-prone without formal verification. In this work,…
We present an automated reasoning framework for synthesizing recursion-free programs using saturation-based theorem proving. Given a functional specification encoded as a first-order logical formula, we use a first-order theorem prover to…
Building consistent distributed systems has largely depended on complex coordination strategies that are not only tricky to implement, but also take a toll on performance as they require nodes to wait for coordination messages. In this…
The cut-elimination procedure for the provability logic is known to be problematic: a L\"ob-like rule keeps cut-formulae intact on reduction, even in the principal case, thereby complicating the proof of termination. In this paper, we…
The operator precedence languages (OPLs) represent the largest known subclass of the context-free languages which enjoys all desirable closure and decidability properties. This includes the decidability of language inclusion, which is the…
We formulate and study a fundamental search and detection problem, Schedule Optimization, motivated by a variety of real-world applications, ranging from monitoring content changes on the web, social networks, and user activities to…
We propose a cut-free cyclic system for Transitive Closure Logic (TCL) based on a form of hypersequents, suitable for automated reasoning via proof search. We show that previously proposed sequent systems are cut-free incomplete for basic…
The Lov\'{a}sz Local Lemma (LLL) is a keystone principle in probability theory, guaranteeing the existence of configurations which avoid a collection $\mathcal B$ of "bad" events which are mostly independent and have low probability. In its…
A sliding window algorithm receives a stream of symbols and has to output at each time instant a certain value which only depends on the last $n$ symbols. If the algorithm is randomized, then at each time instant it produces an incorrect…
The model of asynchronous programming arises in many contexts, from low-level systems software to high-level web programming. We take a language-theoretic perspective and show general decidability and undecidability results for asynchronous…
Structural resolution (or S-resolution) is a newly proposed alternative to SLD-resolution that allows a systematic separation of derivations into term-matching and unification steps. Productive logic programs are those for which…
Lock-free concurrent algorithms guarantee that some concurrent operation will always make progress in a finite number of steps. Yet programmers prefer to treat concurrent code as if it were wait-free, guaranteeing that all operations always…