Symbolic Steps Research Articles

Fast Symbolic Algorithms for Omega-Regular Games under Strong Transition Fairness

We consider fixpoint algorithms for two-player games on graphs with $\omega$-regular winning conditions, where the environment is constrained by a strong transition fairness assumption. Strong transition fairness is a widely occurring special case of strong fairness, which requires that any execution is strongly fair with respect to a specified set of live edges: whenever the source vertex of a live edge is visited infinitely often along a play, the edge itself is traversed infinitely often along the play as well. We show that, surprisingly, strong transition fairness retains the algorithmic characteristics of the fixpoint algorithms for $\omega$-regular games -- the new algorithms have the same alternation depth as the classical algorithms but invoke a new type of predecessor operator. For Rabin games with $k$ pairs, the complexity of the new algorithm is $O(n^{k+2}k!)$ symbolic steps, which is independent of the number of live edges in the strong transition fairness assumption. Further, we show that GR(1) specifications with strong transition fairness assumptions can be solved with a 3-nested fixpoint algorithm, same as the usual algorithm. In contrast, strong fairness necessarily requires increasing the alternation depth depending on the number of fairness assumptions. We get symbolic algorithms for (generalized) Rabin, parity and GR(1) objectives under strong transition fairness assumptions as well as a direct symbolic algorithm for qualitative winning in stochastic $\omega$-regular games that runs in $O(n^{k+2}k!)$ symbolic steps, improving the state of the art. Finally, we have implemented a BDD-based synthesis engine based on our algorithm. We show on a set of synthetic and real benchmarks that our algorithm is scalable, parallelizable, and outperforms previous algorithms by orders of magnitude.

Neuro-symbolic Natural Logic with Introspective Revision for Natural Language Inference

Abstract We introduce a neuro-symbolic natural logic framework based on reinforcement learning with introspective revision. The model samples and rewards specific reasoning paths through policy gradient, in which the introspective revision algorithm modifies intermediate symbolic reasoning steps to discover reward-earning operations as well as leverages external knowledge to alleviate spurious reasoning and training inefficiency. The framework is supported by properly designed local relation models to avoid input entangling, which helps ensure the interpretability of the proof paths. The proposed model has built-in interpretability and shows superior capability in monotonicity inference, systematic generalization, and interpretability, compared with previous models on the existing datasets.

BDD-Based Algorithm for SCC Decomposition of Edge-Coloured Graphs

Edge-coloured directed graphs provide an essential structure for modelling and analysis of complex systems arising in many scientific disciplines (e.g. feature-oriented systems, gene regulatory networks, etc.). One of the fundamental problems for edge-coloured graphs is the detection of strongly connected components, or SCCs. The size of edge-coloured graphs appearing in practice can be enormous both in the number of vertices and colours. The large number of vertices prevents us from analysing such graphs using explicit SCC detection algorithms, such as Tarjan's, which motivates the use of a symbolic approach. However, the large number of colours also renders existing symbolic SCC detection algorithms impractical. This paper proposes a novel algorithm that symbolically computes all the monochromatic strongly connected components of an edge-coloured graph. In the worst case, the algorithm performs $O(p \cdot n \cdot log~n)$ symbolic steps, where $p$ is the number of colours and $n$ is the number of vertices. We evaluate the algorithm using an experimental implementation based on binary decision diagrams (BDDs). Specifically, we use our implementation to explore the SCCs of a large collection of coloured graphs (up to $2^{48}$) obtained from Boolean networks -- a modelling framework commonly appearing in systems biology.

The Influence of Secondary Schoolteachers on Educational Sustainability in Mubi Nigeria.

The implementation of effective public awareness programs for environmental sustainability depends on certain symbolic steps that require the contribution and participation of each stakeholder. This aspect is generally believed to be to a larger extent based on the understanding of the cultural, economic, political and environmental realities of the domain under consideration. This article assesses the level of environmental sustainability awareness of some schools in Mubi, a locality in the extreme North-Eastern part of Nigeria with its unique cultures and attitudes towards the subject. The teacher and his students were targeted in the survey since this is one important institution upon which the future of societies is based. The survey conducted reveals the level of practice of environmental sustainability among this strong media of information dissemination (primary and secondary schools). Areas of concern in the result of the assessment were highlighted. Recommendations in areas of further improvements were suggested.

SSTS: A syntactic tool for pattern search on time series

Nowadays, data scientists are capable of manipulating and extracting complex information from time series data, given the current diversity of tools at their disposal. However, the plethora of tools that target data exploration and pattern search may require an extensive amount of time to develop methods that correspond to the data scientist's reasoning, in order to solve their queries. The development of new methods, tightly related with the reasoning and visual analysis of time series data, is of great relevance to improving complexity and productivity of pattern and query search tasks. In this work, we propose a novel tool, capable of exploring time series data for pattern and query search tasks in a set of 3 symbolic steps: Pre-Processing, Symbolic Connotation and Search. The framework is called SSTS (Symbolic Search in Time Series) and uses regular expression queries to search the desired patterns in a symbolic representation of the signal. By adopting a set of symbolic methods, this approach has the purpose of increasing the expressiveness in solving standard pattern and query tasks, enabling the creation of queries more closely related to the reasoning and visual analysis of the signal. We demonstrate the tool's effectiveness by presenting 9 examples with several types of queries on time series. The SSTS queries were compared with standard code developed in Python, in terms of cognitive effort, vocabulary required, code length, volume, interpretation and difficulty metrics based on the Halstead complexity measures. The results demonstrate that this methodology is a valid approach and delivers a new abstraction layer on data analysis of time series.

Automatic Correction of Dynamic Power Management Architecture in Modern Processors

The increasing demand for lower power forces designers to use sophisticated power management strategies such as multivoltage and power gating which are often accompanied with many design bugs. Correcting such bugs can be a time-consuming process that requires considerable manual efforts. In this paper, we propose a scalable automated method for correcting dynamic power management architectures by an incremental SAT-based mechanism. First, an initial counterexample (CEX) is generated by checking the equivalency between the specification model of the processor and its buggy implementation model. Then, we find two candidate solutions instead of one to satisfy this CEX. If two solutions are not equivalent, we generate new CEX in an iterative process which effectively converges into the final solution. The proposed method enables designers to correct multiple bugs such as missing isolation cells between two power domains, disordering in the sequence of control signals, error in the data restoring or saving, and powering off in always-on domains which are not addressed by existing methods. We have shown the effectiveness of our method on modern processors supporting complex power management mechanisms. The results confirm that our proposed method, respectively, reduces symbolic simulation steps and runtime by 2.33× and 47.93× compared to the state-of-the-art methods.

Mode-Target Games: Reactive Synthesis for Control Applications

In this paper, we introduce a class of linear temporal logic (LTL) specifications for which the problem of synthesizing controllers can be solved in polynomial time. The new class of specifications is an LTL fragment that we term Mode Target (MT) and is inspired by numerous control applications where there are modes and corresponding (possibly multiple) targets for each mode. We formulate the problem of synthesizing a controller enforcing an MT specification as a game and provide an algorithm that requires $O(\sum _i t_i n^2)$ symbolic steps, where $n$ is the number of states in the game graph, and $t_i$ is the number of targets corresponding to mode $i$ .

ECONOMIC RELATIONS BETWEEN THE USSR AND THE FRANCOIST SPAIN IN THE 1960-S

Relations between Spain and the Soviet Union in the XX century had periods of rapid development and quick decline. During the civil war in Spain the ties intensified unprecedentedly, but the rule of Francisco Franco was marked by the transformation of the two states into ideological and political opponents. The period of World War II can be considered as the lowest point in the relationship, when Spanish volunteers fought in the Wehrmacht on the Eastern Front. The situation did not improve after the war, when the Soviet Union proposed the most stringent measures to influence the Franco regime. Nevertheless, since the second half of the 1950s, when both regimes experienced a period of relative liberalization, direct channels of communication, primarily economic, have begun to appear. Together with symbolic steps that the sides exchanged, the development of economic relations contributed significantly to the change. The Soviet Union supplied aluminum, cellu-lose and tractors, Spain exported agricultural products and copper. Since the middle of the 1960s, the range of goods has become more diverse: in Soviet deliveries, oil and oil products have played an increasing role, and Spain has provided more and more consumer goods. In the second half of the 1960s a new sphere has opened for the trade relations between Madrid and Moscow - fishing. Active development of the fishing industry in the USSR required new fishing areas, and the Spanish ports were convenient for basing Soviet fishing vessels. In the end of the decade, the sides signed a number of bilateral treaties regulating the mutual use of coastal infrastruc-ture. Economic ties between the USSR and the francoist Spain began to pave the way for establishing normal relations between the two countries.

Taking Down the Flag Is Just a Start: Toward the Memory-Work of Racial Reconciliation in White Supremacist America

Taking Down the Flag Is Just a StartToward the Memory-Work of Racial Reconciliation in White Supremacist America Joshua F.J. Inwood (bio) and Derek Alderman (bio) On 17 June 2015 Dylann Roof, a self-avowed white supremacist, walked into Emanuel African Methodist Episcopal Church and sat down for a Bible study. After spending forty-five minutes attending the service, he pulled a Glock 41 .45 caliber handgun from his backpack and opened fire, killing nine people. Roof then fled and was ultimately arrested twenty-four hours later in North Carolina. Of the nine killed the oldest was 87 year old Susie Jackson, and the youngest was 26 year old Tywanza Sanders. After his arrest Roof claimed that he assassinated the members of Emanuel AME Church in the hopes of igniting a broader race war. Indeed, photographs later emerged and went viral of Roof engaged in racist exhibitions and hate speech in the past, in particular the flying of the controversial and insensitive Confederate battle flag. In the aftermath of the Charleston massacre, we saw renewed efforts to remove Confederate symbols from across the South’s public spaces, with South Carolina legislators finally voting to remove the flag from the state capitol grounds. In addition, the nation witnessed the grace of survivors in forgiving Roof. These were meaningful and symbolic steps that, thankfully, had the opposite effect than the one the white supremacist shooter had intended. While it is undeniably tragic that nine innocent people had to die before political leaders realized what many African Americans have known and lived with for generations, it is also indicative of a nation that whitewashes the connections between the material realities of white supremacy and its grounding in historical memory. The Confederate flag is a highly charged reminder of legacies of racism that have long been employed by racists to intimidate the black community and to oppose those struggling for racial equality. The banner of the secessionist, pro-slavery southern government had largely faded from memory and sight in the years after the Civil War, but it reappeared not coincidentally after World War II as a symbol of [End Page 9] conservative white resistance to what was then the nascent Civil Rights Movement. African Americans who famously protested segregated bussing in Montgomery, Alabama in 1955 have vivid memories of being pelted with balloons filled with urine, which were thrown from cars and trucks decorated with Confederate flags. In 1959, in the wake of Brown v. Board of Education, school officials in Fairfax, Virginia named and opened a new high school after Confederate general J.E.B. Stuart (Shapiro 2015). Many communities carried out similar not-so-subtle strategies of defending white supremacy under the guise of southern heritage and pride. The landscape has retained major traces of these racist symbols and, as a result of the Charleston Massacre, these symbols are being challenged well beyond the removal of the Confederate flag. As activists and others from across the United States recognize, challenging the legitimacy of publicly displaying Confederate flags and other symbols that legitimize the defense of slavery and white supremacy is certainly the right thing to do. Yet these calls should not be mistaken for a solution to structural inequality. In particular, while state legislators from across the South should be applauded for taking down Confederate symbols, that is not the same thing as addressing the deeply entrenched social and spatial conditions that allow white supremacy to permeate not just the Charleston AME church but wider swaths of American life. This contradictory reality—addressing the symbols of a racist heritage without challenging the foundational histories and geographies of racism—raises questions about the relationship between violence, race and memory (Tyner et al. 2014). These questions are seldom discussed in our post-Charleston Nine social world. Recently, Karen Till has argued that progressive change requires a direct engagement with the trauma of “memory work” in which “individuals and groups may confront and take responsibility for the failures of the democratic state and its violences” (Till 2012, pg. 7). In particular, she highlights the place-based practices of local citizens, activists, educators, artists, and even performers in carrying out the physical, political, and...

Symbolic Aspects in the Literature of Ştefan Augustin Doinaş

Symbolic Aspects in the Literature of Ştefan Augustin Doinaş

Controller Synthesis for Mode-Target Games

Cyber-Physical Systems (CPS) are notoriously difficult to verify due to the intricate interactions between the cyber and the physical components. To address this difficulty, several researchers have argued that the synthesis paradigm is better suited to ensure the correct operation of CPS than the verification paradigm. The key insight of synthesis is that design should be constrained so that resulting systems are easily verified and, ideally, synthesis algorithms should directly provide a proof of correctness.In this paper we present a Linear Temporal Logic fragment inspired by specifications that frequently occur in control applications where we have a set of modes and corresponding targets to be reached for each mode. The synthesis problem for this fragment is formulated as a mode-target game and we show that these games can be solved in polynomial time by providing two embeddings of mode-target games into Generalized Reactivity(1) (GR(1)) games. While solving GR(1) games requires O(mnN2) symbolic steps when we have m assumptions, n guarantees, and a game graph with N states, mode-target games can be solved in O(nN2) symbolic steps when we have n modes and a game graph with N states. These embeddings, however, do not make full use of the specificity of mode-target games. For this reason we investigate in this paper a solution to mode-target games that does not rely on GR(1) embeddings. The resulting algorithm has the same worst case time complexity and we illustrate through experimental results the extent to which it improves upon the algorithms obtained via GR(1) embeddings. In doing so, we highlight the commonalities between mode-target games and GR(1) games while providing additional insight into the solution of GR(1) games.

The Snubs and the ‘Sukkah’: John Lindsay and Jewish Voters in New York City

The Snubs and the ‘Sukkah’:John Lindsay and Jewish Voters in New York City Jeffrey F. Taffet (bio) The Jewish Community as of now stands in opposition to the Mayor’s reelection … Jews are disaffected as citizens, as New Yorkers — or more correctly — as lower middle — and middle class Brooklynites, Bronxites, and Queensites. And they share their complaints, disappointments, and exasperations with others of similar socioeconomic status. They question both the substance and motivation behind the Mayor’s policies and action …1 New York City Mayor John V. Lindsay (governed 1966–1973) needed Jewish voters to win his reelection bid in 1969. But in the months before the election, survey and anecdotal evidence suggested that Jewish support at the polls would not be forthcoming.2 Many Jews had come to believe that Lindsay had not been effective and, more importantly, that he had little interest in supporting their particular interests. Recognizing the necessity of courting Jewish voters, Lindsay took a series of important symbolic steps to reassure Jews that he understood and sympathized with their concerns. Most notable among these was an extraordinary reception he gave in a sukkah for Israeli Prime Minister Golda Meir during her visit to New York in late September of 1969. Lindsay’s advisors believed that this reception was the key factor that helped him win Jewish support and, by extension, the election. In his second term, Lindsay continued to focus on appealing to Jewish voters using the model set by the Meir visit — by embracing their international concerns. This included energetically snubbing foreign leaders whom New York Jews believed had anti-Israel agendas, traveling to Israel, and embracing the nascent Soviet Jewry movement. Lindsay’s approach to these issues reflected the ways in which international and local politics intersected in New York City. In a city [End Page 413] containing large and powerful ethnic communities with ties to foreign countries, Lindsay, like his predecessors and successors, recognized he needed to act as a kind of foreign minister for the city as a way of helping him to connect with ethnic voters. While this meant an occasional trip to Ireland and Italy and, later, to Puerto Rico and the Dominican Republic, issues related to Israel were most significant throughout the postwar period. Many Jewish voters expected that their representatives, even ones on the city level who had little international power, would speak to their concerns about Israel’s future.3 Study of Lindsay’s efforts regarding international politics helps to explain how Jewish political power operated in New York City, where Jews were extraordinarily influential. Eli Lederhendler, in his study of New York Jewish life in the 1950s and 1960s, wrote that the city served as a kind of “Jewish Camelot.” He argued that it was a double urban utopia in which Jews could become leaders in a “cosmopolitan paradise, providing unhindered participation in the life of a world-city” and also a place where they could “build a Jewish cultural center that might sustain the entire Jewish people.”4 New York was both a great secular city that Jews had helped make great, and an object to advance Jewish concerns nationally and internationally. As a result of these two factors, New York City leaders had to make sure that their international policies reflected Jewish sensibilities, just as Jewish New Yorkers had come to understand that the municipal government could be an effective tool in influencing global politics. Many writers have addressed the relationships between Israel and American political systems, often in critical tones.5 While many Jewish [End Page 414] voters were certainly interested in Israel, and did involve themselves in lobbying activities, politicians were not simply pawns. Political leaders attempted to develop their pro-Israel credentials to advance their own electoral prospects. Understanding Lindsay’s actions and how he came to appreciate the links between Israel and city politics thus illuminates the evolution of Jewish involvement in the foreign policy arena. Lindsay and the Jewish Vote Lindsay’s need to attract Jewish voters in the 1969 election was a function of basic electoral and demographic realities in New York City. In 1960, approximately 2.1 million Jews lived in the city, representing about...

Symbolic algorithms for qualitative analysis of Markov decision processes with Büchi objectives

We consider Markov decision processes (MDPs) with Büchi (liveness) objectives. We consider the problem of computing the set of almost-sure winning states from where the objective can be ensured with probability 1. Our contributions are as follows: First, we present the first subquadratic symbolic algorithm to compute the almost-sure winning set for MDPs with Büchi objectives; our algorithm takes \(O(n \cdot\sqrt{m})\) symbolic steps as compared to the previous known algorithm that takes O(n 2) symbolic steps, where n is the number of states and m is the number of edges of the MDP. In practice MDPs have constant out-degree, and then our symbolic algorithm takes \(O(n \cdot\sqrt{n})\) symbolic steps, as compared to the previous known O(n 2) symbolic steps algorithm. Second, we present a new algorithm, namely win-lose algorithm, with the following two properties: (a) the algorithm iteratively computes subsets of the almost-sure winning set and its complement, as compared to all previous algorithms that discover the almost-sure winning set upon termination; and (b) requires \(O(n \cdot\sqrt{K})\) symbolic steps, where K is the maximal number of edges of strongly connected components (scc’s) of the MDP. The win-lose algorithm requires symbolic computation of scc’s. Third, we improve the algorithm for symbolic scc computation; the previous known algorithm takes linear symbolic steps, and our new algorithm improves the constants associated with the linear number of steps. In the worst case the previous known algorithm takes 5⋅n symbolic steps, whereas our new algorithm takes 4⋅n symbolic steps.

Synthesis of Reactive(1) designs

We address the problem of automatically synthesizing digital designs from linear-time specifications. We consider various classes of specifications that can be synthesized with effort quadratic in the number of states of the reactive system, where we measure effort in symbolic steps. The synthesis algorithm is based on a novel type of game called General Reactivity of rank 1 (gr(1)), with a winning condition of the form(□ ◊p1∧⋯∧□ ◊pm)→(□ ◊q1∧⋯∧□ ◊qn), where each pi and qi is a Boolean combination of atomic propositions. We show symbolic algorithms to solve this game, to build a winning strategy and several ways to optimize the winning strategy and to extract a system from it. We also show how to use gr(1) games to solve the synthesis of ltl specifications in many interesting cases. As empirical evidence to the generality and efficiency of our approach we include a significant case study. We describe the formal specifications and the synthesis process applied to a bus arbiter, which is a realistic industrial hardware specification of modest size.

Chinese Assertiveness in the South China Sea and Southeast Asian Responses

This article reviews Chinese assertive behaviour towards the Philippines and Vietnam over South China Sea issues in 2011. The article compares and contrasts Chinese diplomatic behaviour in the period before and after the adoption by ASEAN member states and China of Guidelines for the Implementation the Declaration on Conduct of Parties in the South China Sea in July. In the first period China aggressively asserted its claims to sovereignty by interfering with commercial fishing and oil exploration activities of vessels operating in the Exclusive Economic Zones of Vietnam and the Philippines. Both states resisted Chinese actions. The Philippines allocated increased funding for defence modernization, lobbied ASEAN states and shored up its alliance with the United States. Vietnam too protested Chinese action and undertook symbolic steps to defend national sovereignty. In the second period all states moved to contain South China Sea tensions from affecting their larger bilateral relations. It remains to be seen, however, if proposed confidence building measures will ameliorate Chinese assertiveness.

On the three-state weather model of transmission line failures

Recent work by Billinton et al. has highlighted the importance of employing more than one adverse weather state when modelling transmission line failures by Markov processes. In the present work the structure of the modelling Markov process is identified, allowing the rate matrix to be written in a closed form using Kronecker matrix operations. This approach allows larger models to be handled safely and with ease. The MAXIMA implementation of two asymptotic reliability indices for such systems is addressed, exemplifying the combination of symbolic and numerical steps, perhaps not seen in this context before. It is also indicated how the three-state weather model can be extended to a multi-state model, while retaining the scope of the proposed closed-form expression for the rate matrix. Some possible future work is discussed.

Pakistan in 2006: Safe Center, Dangerous Peripheries

In 2006 Pakistan saw increased ethnic violence in Balochistan, the reassembling and resurgence of Taliban forces across its western and northern borders, the watering down of the draconian Hudood Ordinances, and small symbolic steps toward democratization by the two major opposition leaders.

An Algorithm for Strongly Connected Component Analysis in n log n Symbolic Steps

We present a symbolic algorithm for strongly connected component decomposition. The algorithm performs ( n log n ) image and preimage computations in the worst case, where n is the number of nodes ...

Rank-Based Symbolic Bisimulation: (and Model Checking)

In this paper we propose an efficient symbolic algorithm for the problem of determining the maximum bisimulation on a finite structure. The starting point is an algorithm, on explicit representation of graphs, which saves both time and space exploiting the notion of rank. This notion provides a layering of the input model and allows to proceed bottom-up in the bisimulation computation. In this paper we give a procedure that allows to compute the rank of a graph working on its symbolic representation and requiring a linear number of symbolic steps. Then we embed it in a fully symbolic, rank-driven, bisimulation algorithm. Moreover, we show how the notion of rank can be employed to optimize the CTL Model Checking procedures.