{"title":"On Proof Complexity of Resolution over Polynomial Calculus","authors":"Erfan Khaniki","doi":"10.1145/3506702","DOIUrl":"https://doi.org/10.1145/3506702","url":null,"abstract":"The proof system Res (PCd,R) is a natural extension of the Resolution proof system that instead of disjunctions of literals operates with disjunctions of degree d multivariate polynomials over a ring R with Boolean variables. Proving super-polynomial lower bounds for the size of Res(PC1,R)-refutations of Conjunctive normal forms (CNFs) is one of the important problems in propositional proof complexity. The existence of such lower bounds is even open for Res(PC1,𝔽) when 𝔽 is a finite field, such as 𝔽2. In this article, we investigate Res(PCd,R) and tree-like Res(PCd,R) and prove size-width relations for them when R is a finite ring. As an application, we prove new lower bounds and reprove some known lower bounds for every finite field 𝔽 as follows: (1) We prove almost quadratic lower bounds for Res(PCd,𝔽)-refutations for every fixed d. The new lower bounds are for the following CNFs:(a) Mod q Tseitin formulas (char(𝔽)≠ q) and Flow formulas,(b) Random k-CNFs with linearly many clauses.(2) We also prove super-polynomial (more than nk for any fixed k) and also exponential (2nϵ for an ϵ > 0) lower bounds for tree-like Res(PCd,𝔽)-refutations based on how big d is with respect to n for the following CNFs:(a) Mod q Tseitin formulas (char(𝔽)≠ q) and Flow formulas,(b) Random k-CNFs of suitable densities,(c) Pigeonhole principle and Counting mod q principle. The lower bounds for the dag-like systems are the first nontrivial lower bounds for these systems, including the case d=1. The lower bounds for the tree-like systems were known for the case d=1 (except for the Counting mod q principle, in which lower bounds for the case d> 1 were known too). Our lower bounds extend those results to the case where d> 1 and also give new proofs for the case d=1.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130020206","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Parameterized Complexity of Elimination Distance to First-Order Logic Properties","authors":"F. Fomin, P. Golovach, D. Thilikos","doi":"10.1145/3517129","DOIUrl":"https://doi.org/10.1145/3517129","url":null,"abstract":"The elimination distance to some target graph property P is a general graph modification parameter introduced by Bulian and Dawar. We initiate the study of elimination distances to graph properties expressible in first-order logic. We delimit the problem’s fixed-parameter tractability by identifying sufficient and necessary conditions on the structure of prefixes of first-order logic formulas. Our main result is the following meta-theorem: For every graph property P expressible by a first order-logic formula ( varphi in Sigma _3 ) , that is, of the form ( begin{equation*} varphi =exists x_1exists x_2cdots exists x_r forall y_{1}forall y_{2}cdots forall y_{s} exists z_1exists z_2cdots exists z_t~~ psi ,end{equation*} ) where ( psi ) is a quantifier-free first-order formula, checking whether the elimination distance of a graph to P does not exceed ( k ) , is fixed-parameter tractable parameterized by ( k ) . Properties of graphs expressible by formulas from ( Sigma _3 ) include being of bounded degree, excluding a forbidden subgraph, or containing a bounded dominating set. We complement this theorem by showing that such a general statement does not hold for formulas with even slightly more expressive prefix structure: There are formulas ( varphi in Pi _3 ) , for which computing elimination distance is ( {sf W}[2] ) -hard.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"81 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131725158","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Daniel Gratzer, Evan Cavallo, G. A. Kavvos, Adrien Guatto, L. Birkedal
{"title":"Modalities and Parametric Adjoints","authors":"Daniel Gratzer, Evan Cavallo, G. A. Kavvos, Adrien Guatto, L. Birkedal","doi":"10.1145/3514241","DOIUrl":"https://doi.org/10.1145/3514241","url":null,"abstract":"Birkedal et al. recently introduced dependent right adjoints as an important class of (non-fibered) modalities in type theory. We observe that several aspects of their calculus are left underdeveloped and that it cannot serve as an internal language. We resolve these problems by assuming that the modal context operator is a parametric right adjoint. We show that this hitherto unrecognized structure is common. Based on these discoveries we present a new well-behaved Fitch-style multimodal type theory, which can be used as an internal language. Finally, we apply this syntax to guarded recursion and parametricity.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122073791","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
P. Balbiani, H. van Ditmarsch, Saúl Fernández González
{"title":"Asynchronous Announcements","authors":"P. Balbiani, H. van Ditmarsch, Saúl Fernández González","doi":"10.1145/3481806","DOIUrl":"https://doi.org/10.1145/3481806","url":null,"abstract":"We propose a multi-agent epistemic logic of asynchronous announcements, where truthful announcements are publicly sent but individually received by agents, and in the order in which they were sent. Additional to epistemic modalities the logic contains dynamic modalities for making announcements and for receiving them. What an agent believes is a function of her initial uncertainty and of the announcements she has received. Beliefs need not be truthful, because announcements already made may not yet have been received. As announcements are true when sent, certain message sequences can be ruled out, just like inconsistent cuts in distributed computing. We provide a complete axiomatization for this asynchronous announcement logic (AA). It is a reduction system that also demonstrates that any formula in AA is equivalent to one without dynamic modalities, just as for public announcement logic. A detailed example modelling message exchanging processes in distributed computing in AA closes our investigation.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128706278","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Strategic Knowledge Acquisition","authors":"Kaya Deuser, Pavel Naumov","doi":"10.1145/3459993","DOIUrl":"https://doi.org/10.1145/3459993","url":null,"abstract":"The article proposes a trimodal logical system that can express the strategic ability of coalitions to learn from their experience. The main technical result is the completeness of the proposed system.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114246903","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Kripke Semantics for Intersection Formulas","authors":"Andrej Dudenhefner, P. Urzyczyn","doi":"10.1145/3453481","DOIUrl":"https://doi.org/10.1145/3453481","url":null,"abstract":"We propose a notion of the Kripke-style model for intersection logic. Using a game interpretation, we prove soundness and completeness of the proposed semantics. In other words, a formula is provable (a type is inhabited) if and only if it is forced in every model. As a by-product, we obtain another proof of normalization for the Barendregt–Coppo–Dezani intersection type assignment system.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126500695","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Verification of Distributed Quantum Programs","authors":"Yuan Feng, Sanjiang Li, M. Ying","doi":"10.1145/3517145","DOIUrl":"https://doi.org/10.1145/3517145","url":null,"abstract":"Distributed quantum systems and especially the Quantum Internet have the ever-increasing potential to fully demonstrate the power of quantum computation. This is particularly true given that developing a general-purpose quantum computer is much more difficult than connecting many small quantum devices. One major challenge of implementing distributed quantum systems is programming them and verifying their correctness. In this paper, we propose a CSP-like distributed programming language to facilitate the specification and verification of such systems. After presenting its operational and denotational semantics, we develop a Hoare-style logic for distributed quantum programs and establish its soundness and (relative) completeness with respect to both partial and total correctness. The effectiveness of the logic is demonstrated by its applications in the verification of quantum teleportation and local implementation of non-local CNOT gates, two important algorithms widely used in distributed quantum systems.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126531428","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
B. Larose, B. Martin, P. Marković, D. Paulusma, Siani Smith, Stanislav Živný
{"title":"QCSP on Reflexive Tournaments","authors":"B. Larose, B. Martin, P. Marković, D. Paulusma, Siani Smith, Stanislav Živný","doi":"10.1145/3508069","DOIUrl":"https://doi.org/10.1145/3508069","url":null,"abstract":"We give a complexity dichotomy for the Quantified Constraint Satisfaction Problem ( mathrm{QCSP}(mathrm{H}) ) when ( mathrm{H} ) is a reflexive tournament. It is well known that reflexive tournaments can be split into a sequence of strongly connected components ( mathrm{H}_1,ldots ,mathrm{H}_n ) so that there exists an edge from every vertex of ( mathrm{H}_i ) to every vertex of ( mathrm{H}_j ) if and only if ( ilt j ) . We prove that if ( mathrm{H} ) has both its initial and final strongly connected component (possibly equal) of size 1, then ( mathrm{QCSP}(mathrm{H}) ) is in ( mathsf {NL} ) and otherwise ( mathrm{QCSP}(mathrm{H}) ) is ( mathsf {NP} ) -hard.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121426246","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Meta-theory for Big-step Semantics","authors":"Francesco Dagnino","doi":"10.1145/3522729","DOIUrl":"https://doi.org/10.1145/3522729","url":null,"abstract":"It is well known that big-step semantics is not able to distinguish stuck and non-terminating computations. This is a strong limitation as it makes it very difficult to reason about properties involving infinite computations, such as type soundness, which cannot even be expressed. We show that this issue is only apparent: the distinction between stuck and diverging computations is implicit in any big-step semantics and it just needs to be uncovered. To achieve this goal, we develop a systematic study of big-step semantics: we introduce an abstract definition of what a big-step semantics is, we define a notion of computation by formalizing the evaluation algorithm implicitly associated with any big-step semantics, and we show how to canonically extend a big-step semantics to characterize stuck and diverging computations. Building on these notions, we describe a general proof technique to show that a predicate is sound, that is, it prevents stuck computation, with respect to a big-step semantics. One needs to check three properties relating the predicate and the semantics, and if they hold, the predicate is sound. The extended semantics is essential to establish this meta-logical result but is of no concerns to the user, who only needs to prove the three properties of the initial big-step semantics. Finally, we illustrate the technique by several examples, showing that it is applicable also in cases where subject reduction does not hold, and hence the standard technique for small-step semantics cannot be used.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130345031","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Tzanis Anevlavis, M. Philippe, D. Neider, P. Tabuada
{"title":"Being Correct Is Not Enough: Efficient Verification Using Robust Linear Temporal Logic","authors":"Tzanis Anevlavis, M. Philippe, D. Neider, P. Tabuada","doi":"10.1145/3491216","DOIUrl":"https://doi.org/10.1145/3491216","url":null,"abstract":"While most approaches in formal methods address system correctness, ensuring robustness has remained a challenge. In this article, we present and study the logic rLTL, which provides a means to formally reason about both correctness and robustness in system design. Furthermore, we identify a large fragment of rLTL for which the verification problem can be efficiently solved, i.e., verification can be done by using an automaton, recognizing the behaviors described by the rLTL formula φ, of size at most O(3 |φ |), where |φ | is the length of φ. This result improves upon the previously known bound of O(5|φ |) for rLTL verification and is closer to the LTL bound of O(2|φ |). The usefulness of this fragment is demonstrated by a number of case studies showing its practical significance in terms of expressiveness, the ability to describe robustness, and the fine-grained information that rLTL brings to the process of system verification. Moreover, these advantages come at a low computational overhead with respect to LTL verification.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126965422","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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