Giorgi Japaridze
This paper shows that, even at the most basic level, the parallel, countable branching and uncountable branching recurrences of Computability Logic (see http://www.cis.upenn.edu/~giorgi/cl.html) validate different principles.
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This letter introduces a new, substantially simplified version of the branching recurrence operation of computability logic (see http://www.cis.upenn.edu/~giorgi/cl.html), and proves its equivalence to the old, "canonical" version.
This paper constructs a cirquent calculus system and proves its soundness and completeness with respect to the semantics of computability logic (see http://www.cis.upenn.edu/~giorgi/cl.html). The logical vocabulary of the system consists of negation, parallel conjunction, parallel disjunction, branching recurrence, and branching corecurrence. The article is published in two parts, with (the present) Part I containing preliminaries and a soundness proof, and (the forthcoming) Part II containing a completeness proof.
This paper constructs a cirquent calculus system and proves its soundness and completeness with respect to the semantics of computability logic (see http://www.cis.upenn.edu/~giorgi/cl.html). The logical vocabulary of the system consists of negation, parallel conjunction, parallel disjunction, branching recurrence, and branching corecurrence. The article is published in two parts, with (the previous) Part I containing preliminaries and a soundness proof, and (the present) Part II containing a completeness proof.
This paper introduces a new simplified version of the countable branching recurrence of Computability Logic, proves its equivalence to the old one, and shows that the basic logic induced by it is a proper superset of the basic logic induced by the uncountable branching recurrence. A further result of this paper is showing that the countable branching recurrence is strictly weaker than the uncountable branching recurrence in the sense that the latter logically implies the former but not vice versa.
This paper shows that the basic logic induced by the parallel recurrence of Computability Logic is a proper superset of the basic logic induced by the branching recurrence. The latter is known to be precisely captured by the cirquent calculus system CL15, conjectured by Japaridze to remain sound---but not complete---with parallel recurrence instead of branching recurrence. The present result is obtained by positively verifying that conjecture. A secondary result of the paper is showing that parallel recurrence is strictly weaker than branching recurrence in the sense that, while the latter log…
We introduce a new, substantially simplified version of the toggling-branching recurrence operation of Computability Logic, prove its equivalence to Japaridze's old, "canonical" version, and also prove that both versions preserve the static property of their arguments.
Separating Rank Logic from Polynomial Time
本文通过证明CFI图同构问题无法在秩逻辑中定义但可在CPT中定义，从而将秩逻辑与CPT及多项式时间分离。
We define a notion of Lambda-simulation for coalgebraic modal logics, parametric on the choice Lambda of predicate liftings for a functor T. We show this notion is adequate in several ways: i) it preserves truth of positive formulas, ii) for Lambda a separating set of monotone predicate liftings, the associated notion of Lambda-bisimulation corresponds to T-behavioural equivalence (moreover Lambda-n-bisimulations correspond to T-n-behavioural equivalence), and iii) in fact, for Lambda-separating and T preserving weak pullbacks, difunctional Lambda-bisimulations are T-bisimulations. In essence,…
We investigate the expressive power of the two main kinds of program logics for complex, non-regular program properties found in the literature: those extending propositional dynamic logic (PDL), and those extending the modal mu-calculus. This is inspired by the recent discovery of a decidable program logic called Visibly Pushdown Fixpoint Logic with Chop which extends both the modal mu-calculus and PDL over visibly pushdown languages, which, so far, constituted the ends of two pillars of decidable program logics. Here we show that this logic is not only more expressive than either of its two …
The paper analyzes dynamic epistemic logic from a topological perspective. The main contribution consists of a framework in which dynamic epistemic logic satisfies the requirements for being a topological dynamical system thus interfacing discrete dynamic logics with continuous mappings of dynamical systems. The setting is based on a notion of logical convergence, demonstratively equivalent with convergence in Stone topology. Presented is a flexible, parametrized family of metrics inducing the latter, used as an analytical aid. We show maps induced by action model transformations continuous wi…
We study the separation of positive and negative data examples in terms of description logic concepts in the presence of an ontology. In contrast to previous work, we add a signature that specifies a subset of the symbols that can be used for separation, and we admit individual names in that signature. We consider weak and strong versions of the resulting problem that differ in how the negative examples are treated and we distinguish between separation with and without helper symbols. Within this framework, we compare the separating power of different languages and investigate the complexity o…
In permission logics such as separation logic, the iterated separating conjunction is a quantifier denoting access permission to an unbounded set of heap locations. In contrast to recursive predicates, iterated separating conjunctions do not prescribe a structure on the locations they range over, and so do not restrict how to traverse and modify these locations. This flexibility is important for the verification of random-access data structures such as arrays and data structures that can be traversed in multiple ways such as graphs. Despite its usefulness, no automatic program verifier nativel…
LREC= is an extension of first-order logic with a logarithmic recursion operator. It was introduced by Grohe et al. and shown to capture the complexity class L over trees and interval graphs. It does not capture L in general as it is contained in FPC - fixed-point logic with counting. We show that this containment is strict. In particular, we show that the path systems problem, a classic P-complete problem which is definable in LFP - fixed-point logic - is not definable in LREC= This shows that the logarithmic recursion mechanism is provably weaker than general least fixed points. The proof is…
From Interpolating Formulas to Separating Languages and Back Again
本文探讨了Craig插值的扩展形式，包括在无CIP逻辑中的插值问题，以及形式语言中的分离问题，并展示了这些研究如何相互关联。
Given two languages, a separator is a third language that contains the first one and is disjoint from the second one. We investigate the following decision problem: given two regular input languages of finite words, decide whether there exists a first-order definable separator. We prove that in order to answer this question, sufficient information can be extracted from semigroups recognizing the input languages, using a fixpoint computation. This yields an EXPTIME algorithm for checking first-order separability. Moreover, the correctness proof of this algorithm yields a stronger result, namely…
This paper investigates the satisfiability problem for Separation Logic, with unrestricted nesting of separating conjunctions and implications, for prenex formulae with quantifier prefix in the language $\exists^*\forall^*$, in the cases where the universe of possible locations is either countably infinite or finite. In analogy with first-order logic with uninterpreted predicates and equality, we call this fragment Bernays-Schönfinkel-Ramsey Separation Logic [BSR(SLk)]. We show that, unlike in first-order logic, the (in)finite satisfiability problem is undecidable for BSR(SLk) and we define tw…
Formal reasoning about hashing-based probabilistic data structures often requires reasoning about random variables where when one variable gets larger (such as the number of elements hashed into one bucket), the others tend to be smaller (like the number of elements hashed into the other buckets). This is an example of negative dependence, a generalization of probabilistic independence that has recently found interesting applications in algorithm design and machine learning. Despite the usefulness of negative dependence for the analyses of probabilistic data structures, existing verification m…
In this paper we introduce a class of constraint logic programs such that their termination can be proved by using affine level mappings. We show that membership to this class is decidable in polynomial time.
Dynamic memory issues are hard to locate and may cost much of a development project's efforts and was repeatedly reported similarly afterwards independently by different persons. Verification as one formal method may proof a given program's heap matches a specified dynamic behaviour. Dynamic (or heap) memory, is the region within main memory that is manipulated by program statements like alloc, free and pointer manipulation during program execution. Usually, heap memory is allocated for problems where the amount of used memory is unknown prior to execution. Regions within the heap may be relat…
The Complexity of Defining and Separating Fixpoint Formulae in Modal Logic
研究模态不动点公式的模态可分离性问题，证明在不同模型类上其复杂度从PSpace-完全到TwoExpTime-完全不等，并给出分离子的有效构造算法。
Separating the Wheat from the Chaff: Understanding (In-)Completeness of Proof Mechanisms for Separation Logic with Inductive Definitions
本文研究了分离逻辑中证明机制的不完整性来源，并通过弱分离逻辑的完整性和非标准模型分析，揭示了证明失败的原因。
Separating regular languages with two quantifier alternations
本文研究自动机理论中的分离问题，针对连接层次，证明了基础有限时级别 3/2 的分离可判定，并推广到点深度层次级别 5/2，解决了 Σ₃ 的分离问题。
Computability logic (CL) (see http://www.cis.upenn.edu/~giorgi/cl.html) is a semantical platform and research program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth which it has more traditionally been. Formulas in CL stand for (interactive) computational problems, understood as games between a machine and its environment; logical operators represent operations on such entities; and "truth" is understood as existence of an effective solution, i.e., of an algorithmic winning strategy. The formalism of CL is open-ended, and may undergo series…
Learning temporal formulas from examples is hard
本文研究从示例中学习线性时序逻辑公式的计算复杂性，证明该问题对完整逻辑及几乎所有片段均为NP完全，凸显了表达区分属性的难度，并推动高效启发式方法的探索。
Deciding Boolean Separation Logic via Small Models (Technical Report)
本文提出一种基于小模型边界优化和SMT翻译的分离逻辑判定过程，支持复杂布尔结构与常见链表变体，在符号堆片段上具有竞争力并能处理此前无判定过程的公式。
Separation Logic for Memory Conflict Detection in High-Level Synthesis
研究高级综合中内存冲突检测问题，提出在LLVM IR级别运行的空间验证框架，通过提取表达式建模内存库，利用分离逻辑和SMT预言机保证安全，实现确定性回退，确保硬件免受内存冲突影响。
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